Laziness is the engine of progress. Task generator Part 2
Sometimes I help to carry out mathematical analysis at the first courses and I need to pick up tasks for them to tame. Yes, you can take tasks from the book. But what if you do not find the necessary level of tasks in the books that are at hand?
How to make your own generator of simple tasks for finding limits / derivatives / integrals and will be discussed after kata.
Ps The experience of creating a similar program is described in the previous part.
')
As you can see from the picture, we will generate tasks in pdf using LaTex. There were already many different articles about him , so I'll omit the introductory part. We will implement and create tasks through Pascal (but I will describe the general algorithm and hide all the code in the spoilers).
First you need to define the concept of a polynomial (polynomial), since the trigonometric functions rely on a polynomial. As part of the standard operations you need to enter:
Following the usual polynomial, you will need to enter a polynomial with roots (so that you can search for roots or reduce fractions).
But there will be a peculiarity, since it is necessary to make the same properties not only for the same class, but also for the ordinary polynomial.
And then, by the same type of example, we work with trigonometric functions (including the logarithm and e ^ x).
I will make a reservation in advance that I will not use any trigonometric formulas further. This will increase the complexity not only for the solution, but also for drawing up task diagrams.
To simplify the work with TeX, a separate class was created to later put everything into a separate module.
The class is responsible for:
I will make a reservation in advance that the problem for the derivative and the integral are inverse, so that only one scheme for two problems is needed.
At the beginning of a course of mathematical analysis, the limits (with x-> inf) most often appear: inf / inf, 0/0, inf-inf, a / inf, and a / b.
Hence, the schemes of such tasks should check for understanding the difference forlice .
The task is constructed as P1 (x) / P2 (x) * as x tends to the root P1 (x) (and is not a root of P2 (x)).
* P1 (x) and P2 (x) polynomials with roots from 1 to 3 (sometimes 4th) degrees (random generation)
Simple enough. By analogy with the first example, there is zero in the denominator.
Two polynomials with roots are constructed so that both P (x) have one root. Then, when x tends to this root, the ratio will be 0/0. Hence the need to differentiate P1 (x) and P2 (x) in order to find the correct answer.
An example of the principles of inf-inf, I decided to demonstrate the example of the roots (often found in books, but there are other examples).
Here it is based on the fact that P3 (x) * and P4 (x) * are of one degree, and the solution is to multiply and divide by the conjugate.
* P3 (x), P4 (x) - polynomials under the first degree root
The examples are constructed as follows: the derivative of a function is taken (polynomial / trigonometric function) and its integral must be found (in fact, the function originally taken).
The task can be built in various ways. One of them is to take the trigonometric function T (P (x)) (P (x) polynomial of the second or higher degree) and multiply T (P (x)) by the derivative P (x). Such a technique must be able to notice, so as not to use the decomposition of the integral.
There is a wide variety of typical techniques and examples, but for a minimum assessment of the material’s understanding, such a set rescued me a couple of times. Of course, this set can be expanded and expanded, but this is everyone’s business.
Link to the program: GitHub
There are other tasks in that project that are not described in this article due to their ambiguous work (they are tested and updated).
How to make your own generator of simple tasks for finding limits / derivatives / integrals and will be discussed after kata.
Ps The experience of creating a similar program is described in the previous part.
')
As you can see from the picture, we will generate tasks in pdf using LaTex. There were already many different articles about him , so I'll omit the introductory part. We will implement and create tasks through Pascal (but I will describe the general algorithm and hide all the code in the spoilers).
Let's get started
First you need to define the concept of a polynomial (polynomial), since the trigonometric functions rely on a polynomial. As part of the standard operations you need to enter:
- Addition of polynomials
- Subtracting Polynomials
- Polynomial multiplication
- Erection in the natural degree
- Translation into Tex text
- Derivative
- Integral
Class polynomial
type polynomial = record
st: integer; // degree of polynomial
kof: array of real; // coefficients at x ^ i
function into (x: real): real;
class function operator + (a, b: polynomial): polynomial;
var i, stn: integer;
rez: polynomial;
begin
if (a.st> b.st) then stn: = a.st
else stn: = b.st;
setlength (rez.kof, stn + 1);
for i: = 0 to stn do
rez.kof [i]: = 0;
for i: = 0 to stn do
begin
if (i <= a.st) then
rez.kof [i]: = rez.kof [i] + a.kof [i];
if (i <= b.st) then
rez.kof [i]: = rez.kof [i] + b.kof [i];
end;
rez.st:=stn;
result: = rez;
end;
class function operator- (a, b: polynomial): polynomial;
var i, stn: integer;
rez: polynomial;
begin
if (a.st> b.st) then stn: = a.st
else stn: = b.st;
setlength (rez.kof, stn + 1);
for i: = 0 to stn do
rez.kof [i]: = 0;
for i: = 0 to stn do
begin
if (i <= a.st) then
rez.kof [i]: = rez.kof [i] + a.kof [i];
if (i <= b.st) then
rez.kof [i]: = rez.kof [i] -b.kof [i];
end;
while (rez.kof [stn] = 0) do
begin
setlength (rez.kof, stn);
stn: = stn-1;
end;
rez.st:=stn;
result: = rez;
end;
class function operator * (a, b: polynomial): polynomial;
var i, j, stn: integer;
rez: polynomial;
begin
stn: = a.st + b.st;
setlength (rez.kof, stn + 1);
for i: = 0 to stn do
rez.kof [i]: = 0;
for i: = 0 to a.st do
for j: = 0 to b.st do
begin
rez.kof [i + j]: = rez.kof [i + j] + a.kof [i] * b.kof [j];
end;
while (rez.kof [stn] = 0) do
begin
setlength (rez.kof, stn);
stn: = stn-1;
end;
rez.st:=stn;
result: = rez;
end;
class function operator * (a: integer; b: polynomial): polynomial;
var i: integer;
begin
for i: = 0 to b.st do
b.kof [i]: = a * b.kof [i];
result: = b;
end;
class function operator in (a: polynomial; n: integer): polynomial;
var i: integer;
rez: polynomial;
begin
rez.st:=0;
setlength (rez.kof, 1);
rez.kof [0]: = 1;
for i: = 1 to n do
rez: = rez * a;
result: = rez;
end;
procedure nw (x: integer);
function pltostr: string; // into string variable
procedure derivative; // derivative
procedure integral; // integral
end;
procedure polynomial.nw (x: integer);
var
i: integer;
begin
st: = x;
setlength (kof, st + 1);
for i: = 0 to st do
kof [i]: = random (-10,10);
while (kof [st] = 0) do
kof [st]: = random (-10,10);
end;
procedure polynomial.integral;
var
i: integer;
begin
setlength (kof, st + 2);
for i: = st downto 1 do
kof [i + 1]: = kof [i] / i;
kof [0]: = 0;
st: = st + 1;
setlength (kof, st + 1);
end;
procedure polynomial.derivative;
var
i: integer;
begin
for i: = 1 to st do
kof [i-1]: = kof [i] * i;
st: = st-1;
setlength (kof, st + 1);
end;
st: integer; // degree of polynomial
kof: array of real; // coefficients at x ^ i
function into (x: real): real;
class function operator + (a, b: polynomial): polynomial;
var i, stn: integer;
rez: polynomial;
begin
if (a.st> b.st) then stn: = a.st
else stn: = b.st;
setlength (rez.kof, stn + 1);
for i: = 0 to stn do
rez.kof [i]: = 0;
for i: = 0 to stn do
begin
if (i <= a.st) then
rez.kof [i]: = rez.kof [i] + a.kof [i];
if (i <= b.st) then
rez.kof [i]: = rez.kof [i] + b.kof [i];
end;
rez.st:=stn;
result: = rez;
end;
class function operator- (a, b: polynomial): polynomial;
var i, stn: integer;
rez: polynomial;
begin
if (a.st> b.st) then stn: = a.st
else stn: = b.st;
setlength (rez.kof, stn + 1);
for i: = 0 to stn do
rez.kof [i]: = 0;
for i: = 0 to stn do
begin
if (i <= a.st) then
rez.kof [i]: = rez.kof [i] + a.kof [i];
if (i <= b.st) then
rez.kof [i]: = rez.kof [i] -b.kof [i];
end;
while (rez.kof [stn] = 0) do
begin
setlength (rez.kof, stn);
stn: = stn-1;
end;
rez.st:=stn;
result: = rez;
end;
class function operator * (a, b: polynomial): polynomial;
var i, j, stn: integer;
rez: polynomial;
begin
stn: = a.st + b.st;
setlength (rez.kof, stn + 1);
for i: = 0 to stn do
rez.kof [i]: = 0;
for i: = 0 to a.st do
for j: = 0 to b.st do
begin
rez.kof [i + j]: = rez.kof [i + j] + a.kof [i] * b.kof [j];
end;
while (rez.kof [stn] = 0) do
begin
setlength (rez.kof, stn);
stn: = stn-1;
end;
rez.st:=stn;
result: = rez;
end;
class function operator * (a: integer; b: polynomial): polynomial;
var i: integer;
begin
for i: = 0 to b.st do
b.kof [i]: = a * b.kof [i];
result: = b;
end;
class function operator in (a: polynomial; n: integer): polynomial;
var i: integer;
rez: polynomial;
begin
rez.st:=0;
setlength (rez.kof, 1);
rez.kof [0]: = 1;
for i: = 1 to n do
rez: = rez * a;
result: = rez;
end;
procedure nw (x: integer);
function pltostr: string; // into string variable
procedure derivative; // derivative
procedure integral; // integral
end;
procedure polynomial.nw (x: integer);
var
i: integer;
begin
st: = x;
setlength (kof, st + 1);
for i: = 0 to st do
kof [i]: = random (-10,10);
while (kof [st] = 0) do
kof [st]: = random (-10,10);
end;
procedure polynomial.integral;
var
i: integer;
begin
setlength (kof, st + 2);
for i: = st downto 1 do
kof [i + 1]: = kof [i] / i;
kof [0]: = 0;
st: = st + 1;
setlength (kof, st + 1);
end;
procedure polynomial.derivative;
var
i: integer;
begin
for i: = 1 to st do
kof [i-1]: = kof [i] * i;
st: = st-1;
setlength (kof, st + 1);
end;
Following the usual polynomial, you will need to enter a polynomial with roots (so that you can search for roots or reduce fractions).
But there will be a peculiarity, since it is necessary to make the same properties not only for the same class, but also for the ordinary polynomial.
Polynomial with roots
type polynomialwithroot = record
st: integer; // degree of polynomial
root: array of integer; // roots of a polynomial
kof: array of integer; // coefficients at x ^ i
class function operator + (a, b: polynomialwithroot): polynomial;
var i, stn: integer;
rez: polynomial;
begin
if (a.st> b.st) then stn: = a.st
else stn: = b.st;
setlength (rez.kof, stn + 1);
for i: = 0 to stn do
rez.kof [i]: = 0;
for i: = 0 to stn do
begin
if (i <= a.st) then
rez.kof [i]: = rez.kof [i] + a.kof [i];
if (i <= b.st) then
rez.kof [i]: = rez.kof [i] + b.kof [i];
end;
rez.st:=stn;
result: = rez;
end;
class function operator + (a: polynomialwithroot; b: polynomial): polynomial;
var i, stn: integer;
rez: polynomial;
begin
if (a.st> b.st) then stn: = a.st
else stn: = b.st;
setlength (rez.kof, stn + 1);
for i: = 0 to stn do
rez.kof [i]: = 0;
for i: = 0 to stn do
begin
if (i <= a.st) then
rez.kof [i]: = rez.kof [i] + a.kof [i];
if (i <= b.st) then
rez.kof [i]: = rez.kof [i] + b.kof [i];
end;
rez.st:=stn;
result: = rez;
end;
class function operator + (b: polynomial; a: polynomialwithroot): polynomial;
// var i: integer;
// rez: polynomial;
begin
result: = a + b;
end;
class function operator- (a, b: polynomialwithroot): polynomial;
var i, stn: integer;
rez: polynomial;
begin
if (a.st> b.st) then stn: = a.st
else stn: = b.st;
setlength (rez.kof, stn + 1);
for i: = 0 to stn do
rez.kof [i]: = 0;
for i: = 0 to stn do
begin
if (i <= a.st) then
rez.kof [i]: = rez.kof [i] + a.kof [i];
if (i <= b.st) then
rez.kof [i]: = rez.kof [i] -b.kof [i];
end;
while (rez.kof [stn] = 0) do
begin
setlength (rez.kof, stn);
stn: = stn-1;
end;
rez.st:=stn;
result: = rez;
end;
class function operator- (a: polynomialwithroot; b: polynomial): polynomial;
var i, stn: integer;
rez: polynomial;
begin
if (a.st> b.st) then stn: = a.st
else stn: = b.st;
setlength (rez.kof, stn + 1);
for i: = 0 to stn do
rez.kof [i]: = 0;
for i: = 0 to stn do
begin
if (i <= a.st) then
rez.kof [i]: = rez.kof [i] + a.kof [i];
if (i <= b.st) then
rez.kof [i]: = rez.kof [i] -b.kof [i];
end;
while (rez.kof [stn] = 0) do
begin
setlength (rez.kof, stn);
stn: = stn-1;
end;
rez.st:=stn;
result: = rez;
end;
class function operator- (b: polynomial; a: polynomialwithroot): polynomial;
var i, stn: integer;
rez: polynomial;
begin
if (a.st> b.st) then stn: = a.st
else stn: = b.st;
setlength (rez.kof, stn + 1);
for i: = 0 to stn do
rez.kof [i]: = 0;
for i: = 0 to stn do
begin
if (i <= a.st) then
rez.kof [i]: = rez.kof [i] + a.kof [i];
if (i <= b.st) then
rez.kof [i]: = rez.kof [i] -b.kof [i];
end;
while (rez.kof [stn] = 0) do
begin
setlength (rez.kof, stn);
stn: = stn-1;
end;
rez.st:=stn;
result: = rez;
end;
class function operator * (a, b: polynomialwithroot): polynomialwithroot;
var i, j, stn: integer;
rez: polynomialwithroot;
begin
stn: = a.st + b.st;
setlength (rez.kof, stn + 1);
for i: = 0 to stn do
rez.kof [i]: = 0;
for i: = 0 to a.st do
for j: = 0 to b.st do
begin
rez.kof [i + j]: = rez.kof [i + j] + a.kof [i] * b.kof [j];
end;
while (rez.kof [stn] = 0) do
begin
setlength (rez.kof, stn);
stn: = stn-1;
end;
rez.st:=stn;
setlength (rez.root, rez.st);
for i: = 0 to a.st-1 do
rez.root [i]: = a.root [i];
for i: = 0 to b.st-1 do
rez.root [a.st + i]: = b.root [i];
result: = rez;
end;
class function operator * (a: polynomialwithroot; b: polynomial): polynomial;
var i, j, stn: integer;
rez: polynomial;
begin
stn: = a.st + b.st;
setlength (rez.kof, stn + 1);
for i: = 0 to stn do
rez.kof [i]: = 0;
for i: = 0 to a.st do
for j: = 0 to b.st do
begin
rez.kof [i + j]: = rez.kof [i + j] + a.kof [i] * b.kof [j];
end;
while (rez.kof [stn] = 0) do
begin
setlength (rez.kof, stn);
stn: = stn-1;
end;
rez.st:=stn;
result: = rez;
end;
class function operator * (b: polynomial; a: polynomialwithroot): polynomial;
// var i, j, stn: integer;
// rez: polynomial;
begin
result: = a * b;
end;
class function operator in (a: polynomialwithroot; n: integer): polynomialwithroot;
var i: integer;
rez: polynomialwithroot;
begin
rez: = a;
for i: = 2 to n do
rez: = rez * a;
result: = rez;
end;
procedure nw;
procedure roots (x: integer);
function pltostr: string;
end;
procedure polynomialwithroot.roots (x: integer);
var i: integer;
begin
st: = x;
setlength (root, st);
for i: = 0 to st-1 do
begin
root [i]: = random (-5,5);
end;
nw;
end;
procedure polynomialwithroot.nw;
var
i, j, sum: integer;
tk: array of integer;
dop: integer;
begin
setlength (kof, st + 1);
setlength (tk, st + 1);
for i: = 0 to st-1 do
kof [i]: = 0;
for i: = 0 to st-1 do
begin
for j: = 0 to st do
tk [j]: = 0;
while (tk [st] = 0) do
begin
sum: = 0;
for j: = 0 to st-1 do
sum: = sum + tk [j];
if (sum = (i + 1)) then
begin
dop: = 1;
for j: = 0 to st-1 do
if (tk [j] = 1) then
dop: = dop * root [j];
for j: = 0 to i do
dop: = - dop;
kof [st-i-1]: = kof [st-i-1] + dop;
end;
tk [0]: = tk [0] +1;
for j: = 0 to st-1 do
begin
tk [j + 1]: = tk [j + 1] + (tk [j] div 2);
tk [j]: = tk [j] mod 2;
end;
end;
end;
kof [st]: = 1;
end;
st: integer; // degree of polynomial
root: array of integer; // roots of a polynomial
kof: array of integer; // coefficients at x ^ i
class function operator + (a, b: polynomialwithroot): polynomial;
var i, stn: integer;
rez: polynomial;
begin
if (a.st> b.st) then stn: = a.st
else stn: = b.st;
setlength (rez.kof, stn + 1);
for i: = 0 to stn do
rez.kof [i]: = 0;
for i: = 0 to stn do
begin
if (i <= a.st) then
rez.kof [i]: = rez.kof [i] + a.kof [i];
if (i <= b.st) then
rez.kof [i]: = rez.kof [i] + b.kof [i];
end;
rez.st:=stn;
result: = rez;
end;
class function operator + (a: polynomialwithroot; b: polynomial): polynomial;
var i, stn: integer;
rez: polynomial;
begin
if (a.st> b.st) then stn: = a.st
else stn: = b.st;
setlength (rez.kof, stn + 1);
for i: = 0 to stn do
rez.kof [i]: = 0;
for i: = 0 to stn do
begin
if (i <= a.st) then
rez.kof [i]: = rez.kof [i] + a.kof [i];
if (i <= b.st) then
rez.kof [i]: = rez.kof [i] + b.kof [i];
end;
rez.st:=stn;
result: = rez;
end;
class function operator + (b: polynomial; a: polynomialwithroot): polynomial;
// var i: integer;
// rez: polynomial;
begin
result: = a + b;
end;
class function operator- (a, b: polynomialwithroot): polynomial;
var i, stn: integer;
rez: polynomial;
begin
if (a.st> b.st) then stn: = a.st
else stn: = b.st;
setlength (rez.kof, stn + 1);
for i: = 0 to stn do
rez.kof [i]: = 0;
for i: = 0 to stn do
begin
if (i <= a.st) then
rez.kof [i]: = rez.kof [i] + a.kof [i];
if (i <= b.st) then
rez.kof [i]: = rez.kof [i] -b.kof [i];
end;
while (rez.kof [stn] = 0) do
begin
setlength (rez.kof, stn);
stn: = stn-1;
end;
rez.st:=stn;
result: = rez;
end;
class function operator- (a: polynomialwithroot; b: polynomial): polynomial;
var i, stn: integer;
rez: polynomial;
begin
if (a.st> b.st) then stn: = a.st
else stn: = b.st;
setlength (rez.kof, stn + 1);
for i: = 0 to stn do
rez.kof [i]: = 0;
for i: = 0 to stn do
begin
if (i <= a.st) then
rez.kof [i]: = rez.kof [i] + a.kof [i];
if (i <= b.st) then
rez.kof [i]: = rez.kof [i] -b.kof [i];
end;
while (rez.kof [stn] = 0) do
begin
setlength (rez.kof, stn);
stn: = stn-1;
end;
rez.st:=stn;
result: = rez;
end;
class function operator- (b: polynomial; a: polynomialwithroot): polynomial;
var i, stn: integer;
rez: polynomial;
begin
if (a.st> b.st) then stn: = a.st
else stn: = b.st;
setlength (rez.kof, stn + 1);
for i: = 0 to stn do
rez.kof [i]: = 0;
for i: = 0 to stn do
begin
if (i <= a.st) then
rez.kof [i]: = rez.kof [i] + a.kof [i];
if (i <= b.st) then
rez.kof [i]: = rez.kof [i] -b.kof [i];
end;
while (rez.kof [stn] = 0) do
begin
setlength (rez.kof, stn);
stn: = stn-1;
end;
rez.st:=stn;
result: = rez;
end;
class function operator * (a, b: polynomialwithroot): polynomialwithroot;
var i, j, stn: integer;
rez: polynomialwithroot;
begin
stn: = a.st + b.st;
setlength (rez.kof, stn + 1);
for i: = 0 to stn do
rez.kof [i]: = 0;
for i: = 0 to a.st do
for j: = 0 to b.st do
begin
rez.kof [i + j]: = rez.kof [i + j] + a.kof [i] * b.kof [j];
end;
while (rez.kof [stn] = 0) do
begin
setlength (rez.kof, stn);
stn: = stn-1;
end;
rez.st:=stn;
setlength (rez.root, rez.st);
for i: = 0 to a.st-1 do
rez.root [i]: = a.root [i];
for i: = 0 to b.st-1 do
rez.root [a.st + i]: = b.root [i];
result: = rez;
end;
class function operator * (a: polynomialwithroot; b: polynomial): polynomial;
var i, j, stn: integer;
rez: polynomial;
begin
stn: = a.st + b.st;
setlength (rez.kof, stn + 1);
for i: = 0 to stn do
rez.kof [i]: = 0;
for i: = 0 to a.st do
for j: = 0 to b.st do
begin
rez.kof [i + j]: = rez.kof [i + j] + a.kof [i] * b.kof [j];
end;
while (rez.kof [stn] = 0) do
begin
setlength (rez.kof, stn);
stn: = stn-1;
end;
rez.st:=stn;
result: = rez;
end;
class function operator * (b: polynomial; a: polynomialwithroot): polynomial;
// var i, j, stn: integer;
// rez: polynomial;
begin
result: = a * b;
end;
class function operator in (a: polynomialwithroot; n: integer): polynomialwithroot;
var i: integer;
rez: polynomialwithroot;
begin
rez: = a;
for i: = 2 to n do
rez: = rez * a;
result: = rez;
end;
procedure nw;
procedure roots (x: integer);
function pltostr: string;
end;
procedure polynomialwithroot.roots (x: integer);
var i: integer;
begin
st: = x;
setlength (root, st);
for i: = 0 to st-1 do
begin
root [i]: = random (-5,5);
end;
nw;
end;
procedure polynomialwithroot.nw;
var
i, j, sum: integer;
tk: array of integer;
dop: integer;
begin
setlength (kof, st + 1);
setlength (tk, st + 1);
for i: = 0 to st-1 do
kof [i]: = 0;
for i: = 0 to st-1 do
begin
for j: = 0 to st do
tk [j]: = 0;
while (tk [st] = 0) do
begin
sum: = 0;
for j: = 0 to st-1 do
sum: = sum + tk [j];
if (sum = (i + 1)) then
begin
dop: = 1;
for j: = 0 to st-1 do
if (tk [j] = 1) then
dop: = dop * root [j];
for j: = 0 to i do
dop: = - dop;
kof [st-i-1]: = kof [st-i-1] + dop;
end;
tk [0]: = tk [0] +1;
for j: = 0 to st-1 do
begin
tk [j + 1]: = tk [j + 1] + (tk [j] div 2);
tk [j]: = tk [j] mod 2;
end;
end;
end;
kof [st]: = 1;
end;
And then, by the same type of example, we work with trigonometric functions (including the logarithm and e ^ x).
Trigonometric functions
type sinx = record
x: polynomial;
s: string;
procedure nw;
procedure derivative; // derivative
end;
type cosx = record
x: polynomial;
s: string;
procedure nw;
procedure derivative; // derivative
end;
type tgx = record
x: polynomial;
s: string;
procedure nw;
procedure derivative; // derivative
end;
type ctgx = record
x: polynomial;
s: string;
procedure nw;
procedure derivative; // derivative
end;
type lnx = record
s: string;
x: polynomial;
procedure nw;
procedure derivative;
end;
type ex = record
s: string;
f, x: polynomial;
procedure nw;
procedure derivative;
end;
x: polynomial;
s: string;
procedure nw;
procedure derivative; // derivative
end;
type cosx = record
x: polynomial;
s: string;
procedure nw;
procedure derivative; // derivative
end;
type tgx = record
x: polynomial;
s: string;
procedure nw;
procedure derivative; // derivative
end;
type ctgx = record
x: polynomial;
s: string;
procedure nw;
procedure derivative; // derivative
end;
type lnx = record
s: string;
x: polynomial;
procedure nw;
procedure derivative;
end;
type ex = record
s: string;
f, x: polynomial;
procedure nw;
procedure derivative;
end;
I will make a reservation in advance that I will not use any trigonometric formulas further. This will increase the complexity not only for the solution, but also for drawing up task diagrams.
Something about TeX
To simplify the work with TeX, a separate class was created to later put everything into a separate module.
The class is responsible for:
- Creating a new tex file (creation and introductory block)
- Line-by-line addition of text (at the end of the line will be a transition to a new line)
- Creating a new tex file
- Closing the tex file (closing block and stopping work with the file)
- Create pdf via Tex installed on computer
- Opening pdf file
Module code
type tex = record
namefl: string;
procedure newtex (s: string);
procedure add (s: string);
procedure closetex;
procedure createpdf;
procedure openpdf;
end;
implementation
procedure tex.newtex (s: string);
var
t: text;
begin
namefl: = s;
assign (t, s + '. tex');
rewrite (t);
writeln (t, '\ documentclass [12pt] {article}');
writeln (t, '\ usepackage {amsmath}');
writeln (t, '% \ usepackage [rus] {babel}');
writeln (t, '% \ usepackage [cp1251] {inputenc}');
writeln (t, '\ begin {document}');
close (t);
end;
procedure tex.add (s: string);
var
t: text;
begin
assign (t, namefl + '. tex');
append (t);
writeln (t, '\ [');
writeln (t, s);
writeln (t, '\]');
close (t);
end;
procedure tex.closetex;
var
t: text;
begin
assign (t, namefl + '. tex');
append (t);
writeln (t, '\ end {document}');
close (t);
end;
procedure tex.createpdf;
var
p: System.Diagnostics.Process;
begin
p: = new System.Diagnostics.Process ();
p.StartInfo.FileName: = 'pdflatex';
p.StartInfo.Arguments: = namefl + '. tex';
p.Start ();
end;
procedure tex.openpdf;
var
p: System.Diagnostics.Process;
begin
p: = new System.Diagnostics.Process ();
p.StartInfo.FileName: = namefl + '. pdf';
p.Start ();
end;
namefl: string;
procedure newtex (s: string);
procedure add (s: string);
procedure closetex;
procedure createpdf;
procedure openpdf;
end;
implementation
procedure tex.newtex (s: string);
var
t: text;
begin
namefl: = s;
assign (t, s + '. tex');
rewrite (t);
writeln (t, '\ documentclass [12pt] {article}');
writeln (t, '\ usepackage {amsmath}');
writeln (t, '% \ usepackage [rus] {babel}');
writeln (t, '% \ usepackage [cp1251] {inputenc}');
writeln (t, '\ begin {document}');
close (t);
end;
procedure tex.add (s: string);
var
t: text;
begin
assign (t, namefl + '. tex');
append (t);
writeln (t, '\ [');
writeln (t, s);
writeln (t, '\]');
close (t);
end;
procedure tex.closetex;
var
t: text;
begin
assign (t, namefl + '. tex');
append (t);
writeln (t, '\ end {document}');
close (t);
end;
procedure tex.createpdf;
var
p: System.Diagnostics.Process;
begin
p: = new System.Diagnostics.Process ();
p.StartInfo.FileName: = 'pdflatex';
p.StartInfo.Arguments: = namefl + '. tex';
p.Start ();
end;
procedure tex.openpdf;
var
p: System.Diagnostics.Process;
begin
p: = new System.Diagnostics.Process ();
p.StartInfo.FileName: = namefl + '. pdf';
p.Start ();
end;
Task map
I will make a reservation in advance that the problem for the derivative and the integral are inverse, so that only one scheme for two problems is needed.
Limits
At the beginning of a course of mathematical analysis, the limits (with x-> inf) most often appear: inf / inf, 0/0, inf-inf, a / inf, and a / b.
Hence, the schemes of such tasks should check for understanding the difference for
1. An example where the answer is zero
The task is constructed as P1 (x) / P2 (x) * as x tends to the root P1 (x) (and is not a root of P2 (x)).
* P1 (x) and P2 (x) polynomials with roots from 1 to 3 (sometimes 4th) degrees (random generation)
2. Zero in the denominator
Simple enough. By analogy with the first example, there is zero in the denominator.
3. Zero in the numerator and denominator
Two polynomials with roots are constructed so that both P (x) have one root. Then, when x tends to this root, the ratio will be 0/0. Hence the need to differentiate P1 (x) and P2 (x) in order to find the correct answer.
4. Infinity minus infinity
An example of the principles of inf-inf, I decided to demonstrate the example of the roots (often found in books, but there are other examples).
Here it is based on the fact that P3 (x) * and P4 (x) * are of one degree, and the solution is to multiply and divide by the conjugate.
* P3 (x), P4 (x) - polynomials under the first degree root
Derivatives and integrals
"Take and think"
The examples are constructed as follows: the derivative of a function is taken (polynomial / trigonometric function) and its integral must be found (in fact, the function originally taken).
Method of a sly look
The task can be built in various ways. One of them is to take the trigonometric function T (P (x)) (P (x) polynomial of the second or higher degree) and multiply T (P (x)) by the derivative P (x). Such a technique must be able to notice, so as not to use the decomposition of the integral.
Task Generation Code
unit taskMath;
interface
uses mathUnit;
type taskderivative = record
task: string;
answer: string;
end;
type tasklimits = record
task: string;
answer: string;
end;
function taskintegral1 (var s: string): string;
function tasklimits1 (var s: string): string;
function tasklimits2 (var s: string): string;
function tasklimits3 (var s: string): string;
function tasklimits4 (var s: string): string;
function taskderivative1 (var s: string): string;
function taskderivative2 (var s: string): string;
procedure rand (var x: taskderivative);
procedure rand (var x: tasklimits);
implementation
function correct (s: string): string;
var i: integer;
begin
for i: = 1 to length (s) do
case s [i] of
'{': s [i]: = '(';
'}': s [i]: = ')';
end;
result: = s;
end;
function tasklimits1 (var s: string): string;
var
p1, p2: polynomialwithroot;
i: integer;
x: integer;
rez: string;
k1, k2, r1, r2: integer;
begin
randomize;
p1.roots (random (1,3));
p2.roots (random (1,3));
i: = random (p1.st) -1;
for i: = i downto 0 do
p2.root [random (p2.st)]: = p1.root [random (p1.st)];
i: = random (p1.st) + random (p2.st);
if (i> p1.st-1) then
begin
x: = p2.root [i- (p1.st-1)];
end
else
x: = p1.root [i];
p1.nw;
p2.nw;
rez: = 'Find: \; lim_ {x \ to \!' + inttostr (x) + '} \ quad \ frac {' + p1.pltostr + '} {' + p2.pltostr + '}';
k1: = 0;
k2: = 0;
r1: = 1;
r2: = 1;
s: = 'When \; abbreviations \; (x - '+ inttostr (x) +') \; it turns out \; ';
for i: = 0 to p1.st-1 do
if (p1.kof [i] = x) then
inc (k1)
else
r1: = r1 * (x-p1.kof [i]);
for i: = 0 to p2.st-1 do
if (p2.kof [i] = x) then
inc (k2)
else
r2: = r2 * (x-p2.kof [i]);
if (k1> k2) then
s: = '0'; // s: = s + 'null';
if (k2> k1) then
s: = 'inf'; // s: = s + 'null \; at\; denominator \; and\; it turns out \; infinity';
if (k1 = k2) then
s: = inttostr (r1) + '/' + inttostr (r2); // s: = s + 'number \;' + floattostr (r1 / r2);
s: = correct (s);
result: = rez;
end;
function tasklimits2 (var s: string): string;
var
f: polynomialwithroot;
g, x: polynomial;
st: integer;
rez, answ: string;
begin
f.roots (random (1,2));
g.nw (random (1,2));
x.nw (random (1,2));
st: = f.root [random (0, f.st-1)];
rez: = 'Find: \; lim_ {x \ to \!' + inttostr (st) + '} \ quad \ frac {' + (f * g) .pltostr + '} {' + (f * x) .pltostr + '}';
s: = floattostr (g.into (st)) + '/' + floattostr (x.into (st));
s: = correct (s);
result: = rez;
end;
function tasklimits3 (var s: string): string;
var
f, g: sqrnpolynomial;
x: polynomial;
rez, answ: string;
begin
f.nw (random (1,4), 2);
g.nw (fxst, 2);
x: = fx-gx;
rez: = 'Find: \; lim_ {x \ to \ infty} \ quad' + f.s + '-' + gs;
if (x.st + 1 = fxst) then
s: = floattostr (x.kof [x.st]) + '/' + floattostr (gxkof [gxst] + fxkof [gxst])
else
s: = '0';
s: = correct (s);
result: = rez;
end;
function tasklimits4 (var s: string): string;
var
f, g: polynomialwithroot;
kf1, kf2: polynomial;
a, i, j, num: integer;
rez, add: string;
begin
f.roots (random (1,2));
g.roots (random ((f.st), 3));
num: = random (1, f.st-1);
for i: = 0 to num-1 do
g.root [i]: = f.root [i];
g.nw;
// writeln (num);
sleep (1000);
num: = 0;
for i: = 0 to f.st-1 do
for j: = 0 to g.st-1 do
if (f.kof [i] = g.kof [j]) then num + = 1;
// writeln (num);
// sleep (1000);
kf1.nw (random (1,2));
kf2.nw (0);
a: = random (2,5);
add: = '\ frac {' + (kf1 + kf2) .pltostr + '} {' + kf1.pltostr + '}';
for i: = 1 to length (s) do
if (add [i] = 'x') then add [i]: = 'n';
rez: = 'Find \; x, \; when: \; lim_ {n \ to \ infty} \ quad '+
add + '\ frac {(' + f.pltostr + ') ^ {n ^' + inttostr (a) + '}} {(' + g.pltostr + ') ^ {n ^' + inttostr (a) + '}} = e ^ {'+ floattostr (kf2.kof [0]) +'} ';
s: = inttostr (num);
result: = rez;
end;
function taskintegral1 (var s: string): string;
var
tr1: sinx;
tr2: cosx;
tr3: tgx;
tr4: ctgx;
f, g: polynomial;
r: integer;
rez: string;
begin
rez: = 'Find \; \ int';
r: = random (1,5);
case r of
1: begin
tr1.x.nw (random (1,3));
tr1.nw;
s: = tr1.s;
tr1.derivative;
rez: = rez + tr1.s + '\; dx';
end;
2: begin
tr2.x.nw (random (1,3));
tr2.nw;
s: = tr2.s;
tr2.derivative;
rez: = rez + tr2.s + '\; dx';
end;
3: begin
tr3.x.nw (random (1,3));
tr3.nw;
s: = tr3.s;
tr3.derivative;
rez: = rez + tr3.s + '\; dx';
end;
4: begin
tr4.x.nw (random (1,3));
tr4.nw;
s: = tr4.s;
tr4.derivative;
rez: = rez + tr4.s + '\; dx';
end;
5: begin
r: = random (1,2);
f.nw (random (1,3));
rez: = rez + '(' + f.pltostr + ')';
while (r <> 0) do
begin
g.nw (random (1,3));
f: = f * g;
rez: = rez + '(' + g.pltostr + ')';
r: = r-1;
end;
f.integral;
s: = correct (f.pltostr);
rez: = rez + '\; dx';
end;
end;
s: = correct (s);
result: = rez;
end;
function taskderivative1 (var s: string): string;
var
sinx1, sinx2: sinx;
cosx1, cosx2: cosx;
tgx1, tgx2: tgx;
ctgx1, ctgx2: ctgx;
f, g: polynomial;
r: integer;
rez: string;
bg, answ: string;
begin
randomize;
sinx1.x.nw (random (1,3));
sinx1.nw;
sinx2: = sinx1;
sinx2.derivative;
tgx1.x.nw (random (1,3));
tgx1.nw;
tgx2: = tgx1;
tgx2.derivative;
cosx1.x.nw (random (1,3));
cosx1.nw;
cosx2: = cosx1;
cosx2.derivative;
ctgx1.x.nw (random (1,3));
ctgx1.nw;
ctgx2: = ctgx1;
ctgx2.derivative;
r: = random (1,4);
case r of
1: begin
rez: = rez + sinx1.s;
answ: = sinx2.s;
end;
2: begin
rez: = rez + cosx1.s;
answ: = cosx2.s;
end;
3: begin
rez: = rez + tgx1.s;
answ: = '(' + tgx2.x.pltostr + ') / (cos (' + tgx1.x.pltostr + ') ^ 2)';
end;
4: begin
rez: = rez + ctgx1.s;
answ: = '(' + (- 1 * ctgx2.x) .pltostr + ')) / (sin (' + ctgx1.x.pltostr + ') ^ 2)';
end;
end;
bg: = rez;
rez: = 'Find \; \ frac {d} {dx} \; ('+ rez;
rez: = rez + ')';
r: = random (1,2);
f.nw (random (1,3));
while (r> 0) do
begin
g.nw (random (1,3));
rez: = rez + '(';
rez: = rez + g.pltostr;
rez: = rez + ')';
f: = f * g;
r: = r-1;
end;
rez: = rez + ')';
answ: = '(' + answ + ') * (' + g.pltostr + ') + (';
g.derivative;
answ: = answ + bg + ') * (' + g.pltostr + ')';
s: = answ;
s: = correct (s);
result: = rez;
end;
function taskderivative2 (var s: string): string;
var
sinx1, sinx2: sinx;
cosx1, cosx2: cosx;
tgx1, tgx2: tgx;
ctgx1, ctgx2: ctgx;
f, g, st: polynomial;
r: integer;
rez: string;
answ, bg: string;
begin
randomize;
sinx1.x.nw (random (1,3));
sinx1.nw;
sinx2: = sinx1;
sinx2.derivative;
tgx1.x.nw (random (1,3));
tgx1.nw;
tgx2: = tgx1;
tgx2.derivative;
cosx1.x.nw (random (1,3));
cosx1.nw;
cosx2: = cosx1;
cosx2.derivative;
ctgx1.x.nw (random (1,3));
ctgx1.nw;
ctgx2: = ctgx1;
ctgx2.derivative;
r: = random (1,4);
case r of
1: begin
rez: = rez + sinx1.s;
answ: = sinx2.s;
end;
2: begin
rez: = rez + cosx1.s;
answ: = cosx2.s;
end;
3: begin
rez: = rez + tgx1.s;
answ: = '(' + tgx2.x.pltostr + ') / (cos (' + tgx1.x.pltostr + ') ^ 2)';
end;
4: begin
rez: = rez + ctgx1.s;
answ: = '(' + (- 1 * ctgx2.x) .pltostr + ')) / (sin (' + ctgx1.x.pltostr + ') ^ 2)';
end;
end;
bg: = rez;
rez: = 'Find \; \ frac {d} {dx} \; ('+ rez;
rez: = rez + ') ^ {';
f.nw (random (1,3));
rez: = rez + f.pltostr + '}';
st: = f;
st.derivative;
answ: = '((' + bg + ') ^ {' + f.pltostr + '}) * ((' + st.pltostr + ') * ln (' + bg + ') + (' + f.pltostr + ') * ( '+ answ +') / ('+ bg +') ';
s: = answ;
s: = correct (s);
result: = rez;
end;
procedure rand (var x: taskderivative);
var
r: integer;
begin
randomize;
r: = random (1,2);
case r of
1: x.task: = taskderivative1 (x.answer);
2: x.task: = taskderivative2 (x.answer);
end;
end;
procedure rand (var x: tasklimits);
var
r: integer;
begin
randomize;
r: = random (1,4);
case r of
1: x.task: = tasklimits1 (x.answer);
2: x.task: = tasklimits2 (x.answer);
3: x.task: = tasklimits3 (x.answer);
4: x.task: = tasklimits4 (x.answer);
end;
end;
end.
interface
uses mathUnit;
type taskderivative = record
task: string;
answer: string;
end;
type tasklimits = record
task: string;
answer: string;
end;
function taskintegral1 (var s: string): string;
function tasklimits1 (var s: string): string;
function tasklimits2 (var s: string): string;
function tasklimits3 (var s: string): string;
function tasklimits4 (var s: string): string;
function taskderivative1 (var s: string): string;
function taskderivative2 (var s: string): string;
procedure rand (var x: taskderivative);
procedure rand (var x: tasklimits);
implementation
function correct (s: string): string;
var i: integer;
begin
for i: = 1 to length (s) do
case s [i] of
'{': s [i]: = '(';
'}': s [i]: = ')';
end;
result: = s;
end;
function tasklimits1 (var s: string): string;
var
p1, p2: polynomialwithroot;
i: integer;
x: integer;
rez: string;
k1, k2, r1, r2: integer;
begin
randomize;
p1.roots (random (1,3));
p2.roots (random (1,3));
i: = random (p1.st) -1;
for i: = i downto 0 do
p2.root [random (p2.st)]: = p1.root [random (p1.st)];
i: = random (p1.st) + random (p2.st);
if (i> p1.st-1) then
begin
x: = p2.root [i- (p1.st-1)];
end
else
x: = p1.root [i];
p1.nw;
p2.nw;
rez: = 'Find: \; lim_ {x \ to \!' + inttostr (x) + '} \ quad \ frac {' + p1.pltostr + '} {' + p2.pltostr + '}';
k1: = 0;
k2: = 0;
r1: = 1;
r2: = 1;
s: = 'When \; abbreviations \; (x - '+ inttostr (x) +') \; it turns out \; ';
for i: = 0 to p1.st-1 do
if (p1.kof [i] = x) then
inc (k1)
else
r1: = r1 * (x-p1.kof [i]);
for i: = 0 to p2.st-1 do
if (p2.kof [i] = x) then
inc (k2)
else
r2: = r2 * (x-p2.kof [i]);
if (k1> k2) then
s: = '0'; // s: = s + 'null';
if (k2> k1) then
s: = 'inf'; // s: = s + 'null \; at\; denominator \; and\; it turns out \; infinity';
if (k1 = k2) then
s: = inttostr (r1) + '/' + inttostr (r2); // s: = s + 'number \;' + floattostr (r1 / r2);
s: = correct (s);
result: = rez;
end;
function tasklimits2 (var s: string): string;
var
f: polynomialwithroot;
g, x: polynomial;
st: integer;
rez, answ: string;
begin
f.roots (random (1,2));
g.nw (random (1,2));
x.nw (random (1,2));
st: = f.root [random (0, f.st-1)];
rez: = 'Find: \; lim_ {x \ to \!' + inttostr (st) + '} \ quad \ frac {' + (f * g) .pltostr + '} {' + (f * x) .pltostr + '}';
s: = floattostr (g.into (st)) + '/' + floattostr (x.into (st));
s: = correct (s);
result: = rez;
end;
function tasklimits3 (var s: string): string;
var
f, g: sqrnpolynomial;
x: polynomial;
rez, answ: string;
begin
f.nw (random (1,4), 2);
g.nw (fxst, 2);
x: = fx-gx;
rez: = 'Find: \; lim_ {x \ to \ infty} \ quad' + f.s + '-' + gs;
if (x.st + 1 = fxst) then
s: = floattostr (x.kof [x.st]) + '/' + floattostr (gxkof [gxst] + fxkof [gxst])
else
s: = '0';
s: = correct (s);
result: = rez;
end;
function tasklimits4 (var s: string): string;
var
f, g: polynomialwithroot;
kf1, kf2: polynomial;
a, i, j, num: integer;
rez, add: string;
begin
f.roots (random (1,2));
g.roots (random ((f.st), 3));
num: = random (1, f.st-1);
for i: = 0 to num-1 do
g.root [i]: = f.root [i];
g.nw;
// writeln (num);
sleep (1000);
num: = 0;
for i: = 0 to f.st-1 do
for j: = 0 to g.st-1 do
if (f.kof [i] = g.kof [j]) then num + = 1;
// writeln (num);
// sleep (1000);
kf1.nw (random (1,2));
kf2.nw (0);
a: = random (2,5);
add: = '\ frac {' + (kf1 + kf2) .pltostr + '} {' + kf1.pltostr + '}';
for i: = 1 to length (s) do
if (add [i] = 'x') then add [i]: = 'n';
rez: = 'Find \; x, \; when: \; lim_ {n \ to \ infty} \ quad '+
add + '\ frac {(' + f.pltostr + ') ^ {n ^' + inttostr (a) + '}} {(' + g.pltostr + ') ^ {n ^' + inttostr (a) + '}} = e ^ {'+ floattostr (kf2.kof [0]) +'} ';
s: = inttostr (num);
result: = rez;
end;
function taskintegral1 (var s: string): string;
var
tr1: sinx;
tr2: cosx;
tr3: tgx;
tr4: ctgx;
f, g: polynomial;
r: integer;
rez: string;
begin
rez: = 'Find \; \ int';
r: = random (1,5);
case r of
1: begin
tr1.x.nw (random (1,3));
tr1.nw;
s: = tr1.s;
tr1.derivative;
rez: = rez + tr1.s + '\; dx';
end;
2: begin
tr2.x.nw (random (1,3));
tr2.nw;
s: = tr2.s;
tr2.derivative;
rez: = rez + tr2.s + '\; dx';
end;
3: begin
tr3.x.nw (random (1,3));
tr3.nw;
s: = tr3.s;
tr3.derivative;
rez: = rez + tr3.s + '\; dx';
end;
4: begin
tr4.x.nw (random (1,3));
tr4.nw;
s: = tr4.s;
tr4.derivative;
rez: = rez + tr4.s + '\; dx';
end;
5: begin
r: = random (1,2);
f.nw (random (1,3));
rez: = rez + '(' + f.pltostr + ')';
while (r <> 0) do
begin
g.nw (random (1,3));
f: = f * g;
rez: = rez + '(' + g.pltostr + ')';
r: = r-1;
end;
f.integral;
s: = correct (f.pltostr);
rez: = rez + '\; dx';
end;
end;
s: = correct (s);
result: = rez;
end;
function taskderivative1 (var s: string): string;
var
sinx1, sinx2: sinx;
cosx1, cosx2: cosx;
tgx1, tgx2: tgx;
ctgx1, ctgx2: ctgx;
f, g: polynomial;
r: integer;
rez: string;
bg, answ: string;
begin
randomize;
sinx1.x.nw (random (1,3));
sinx1.nw;
sinx2: = sinx1;
sinx2.derivative;
tgx1.x.nw (random (1,3));
tgx1.nw;
tgx2: = tgx1;
tgx2.derivative;
cosx1.x.nw (random (1,3));
cosx1.nw;
cosx2: = cosx1;
cosx2.derivative;
ctgx1.x.nw (random (1,3));
ctgx1.nw;
ctgx2: = ctgx1;
ctgx2.derivative;
r: = random (1,4);
case r of
1: begin
rez: = rez + sinx1.s;
answ: = sinx2.s;
end;
2: begin
rez: = rez + cosx1.s;
answ: = cosx2.s;
end;
3: begin
rez: = rez + tgx1.s;
answ: = '(' + tgx2.x.pltostr + ') / (cos (' + tgx1.x.pltostr + ') ^ 2)';
end;
4: begin
rez: = rez + ctgx1.s;
answ: = '(' + (- 1 * ctgx2.x) .pltostr + ')) / (sin (' + ctgx1.x.pltostr + ') ^ 2)';
end;
end;
bg: = rez;
rez: = 'Find \; \ frac {d} {dx} \; ('+ rez;
rez: = rez + ')';
r: = random (1,2);
f.nw (random (1,3));
while (r> 0) do
begin
g.nw (random (1,3));
rez: = rez + '(';
rez: = rez + g.pltostr;
rez: = rez + ')';
f: = f * g;
r: = r-1;
end;
rez: = rez + ')';
answ: = '(' + answ + ') * (' + g.pltostr + ') + (';
g.derivative;
answ: = answ + bg + ') * (' + g.pltostr + ')';
s: = answ;
s: = correct (s);
result: = rez;
end;
function taskderivative2 (var s: string): string;
var
sinx1, sinx2: sinx;
cosx1, cosx2: cosx;
tgx1, tgx2: tgx;
ctgx1, ctgx2: ctgx;
f, g, st: polynomial;
r: integer;
rez: string;
answ, bg: string;
begin
randomize;
sinx1.x.nw (random (1,3));
sinx1.nw;
sinx2: = sinx1;
sinx2.derivative;
tgx1.x.nw (random (1,3));
tgx1.nw;
tgx2: = tgx1;
tgx2.derivative;
cosx1.x.nw (random (1,3));
cosx1.nw;
cosx2: = cosx1;
cosx2.derivative;
ctgx1.x.nw (random (1,3));
ctgx1.nw;
ctgx2: = ctgx1;
ctgx2.derivative;
r: = random (1,4);
case r of
1: begin
rez: = rez + sinx1.s;
answ: = sinx2.s;
end;
2: begin
rez: = rez + cosx1.s;
answ: = cosx2.s;
end;
3: begin
rez: = rez + tgx1.s;
answ: = '(' + tgx2.x.pltostr + ') / (cos (' + tgx1.x.pltostr + ') ^ 2)';
end;
4: begin
rez: = rez + ctgx1.s;
answ: = '(' + (- 1 * ctgx2.x) .pltostr + ')) / (sin (' + ctgx1.x.pltostr + ') ^ 2)';
end;
end;
bg: = rez;
rez: = 'Find \; \ frac {d} {dx} \; ('+ rez;
rez: = rez + ') ^ {';
f.nw (random (1,3));
rez: = rez + f.pltostr + '}';
st: = f;
st.derivative;
answ: = '((' + bg + ') ^ {' + f.pltostr + '}) * ((' + st.pltostr + ') * ln (' + bg + ') + (' + f.pltostr + ') * ( '+ answ +') / ('+ bg +') ';
s: = answ;
s: = correct (s);
result: = rez;
end;
procedure rand (var x: taskderivative);
var
r: integer;
begin
randomize;
r: = random (1,2);
case r of
1: x.task: = taskderivative1 (x.answer);
2: x.task: = taskderivative2 (x.answer);
end;
end;
procedure rand (var x: tasklimits);
var
r: integer;
begin
randomize;
r: = random (1,4);
case r of
1: x.task: = tasklimits1 (x.answer);
2: x.task: = tasklimits2 (x.answer);
3: x.task: = tasklimits3 (x.answer);
4: x.task: = tasklimits4 (x.answer);
end;
end;
end.
Summing up
There is a wide variety of typical techniques and examples, but for a minimum assessment of the material’s understanding, such a set rescued me a couple of times. Of course, this set can be expanded and expanded, but this is everyone’s business.
Link to the program: GitHub
There are other tasks in that project that are not described in this article due to their ambiguous work (they are tested and updated).
Source: https://habr.com/ru/post/314924/
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