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Integrade the function f(x) = 1/(x^2 - 5x +6) with respect to x.

First, we need to factorise the denominator and therefore we use this formula: x 1,2 =[ -b + sqrt(b 2 -4 a c) ]/ (2a). You obtain two roots, x = 2 and x=3 and the integration is simplified to : 1/[(x-2)(x-3)...
EE
Answered by Efstathios E. • Maths tutor
1802 Views

Differentiate f(x)= 3y^2 + ln (x) + sin x

We have derivative rules. Some of them involve:If f(x)= (x) a => f'(x)= a*x a-1 If f(x)= ln x=> f'(x)= 1/xIf f(x)= sin x=> f'(x)=cos xTherefore, f(x)= 6y+1/x+cos x
DC
Answered by Daria C. • Maths tutor
1624 Views

Prove Wilson's Theorem, i.e. (p-1)! = -1 (mod p) for any prime number p.

Claim : For any prime p: (p-1)! = -1 (mod p) Proof: For p=2: 1! = 1 so the equality obviously holds. Therefore, we need to consider cases when p is odd. Let's consider set: {1, ... , p-1}. With operation * m...
MP
Answered by Mateusz P. • Maths tutor
8153 Views

Find the cross product between two unit vectors a and b.

First write out the unit vectors in I, j, and k form. Then put these values into a matrix. Then find the determinant of the matrix. Then you will have reached your answer. I couldn't figure out how to show t...
NL
Answered by Nicholas L. • Maths tutor
1830 Views

Is there any rational number whose square is 2?

We all know the the square root of 2 is irrational. So, the answer should be no. But how do we prove it?Let's assume for contradiction that x 2 =2 and that x is rational. Then x can be expressed as a rationa...
AS
Answered by Andrei S. • Maths tutor
13437 Views