## 300 Reputation

12 years, 195 days

## Subtitution in expression...

How to subs t = cos(2*x) in expression A:= cos(x)^2 + cos(4*x)? Please help me. Thank you.

## How to define a function?...

Maple

I have a function

`f:=x->(x^2 + 2*m*x + m + 1)/(x -1);`
`Now I want to define a function as simplify(diff(f(x),x)), i did `
`g:=x->simplify(diff(f(x),x)). Then, i could not calculate g(3). Please help me. Thank you.`

## Real solution of a equation...

Please write a code for the prolem:

Find the all values of paramater m for which the equation

(x-2)*(x^2 - 2*m*x + 5*m - 6) = 0 (x is unknown)

has three diffenrent real solutions.

## Equation of a plane (10)...

Maple

Please write for me another code for the following problem:
Write the equation of the plane (P) passing through the line (d): x = -t -1, y = t + 3, z = 2*t + 2, (P) cuts the axis Ox at A and the axis Oy at B (A, B different form origin O) so that OA = 2OB.

This is my code

restart:

f:=(x,y,z)->a*x+b*y+c*z+d:

A:=f(m,0,0):

B:=f(0,n,0):

C:=f(-1,3,2):

## Command minimize...

Maple

I used the command minimize such

minimize(3*x^2+2*m*x+2*m^2-3*m-6,1 <= x)

But it can not. How can i find the least of the function g:=x>3*x^2+2*m*x+2*m^2-3*m-6,  here x >=1.