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Maths
A Level

How do you find the integral of sin^2(x) dx?

Sin^2(x) cannot be integrated in its current form so you must use trigonometric identities to change sin^2(x) into something else.

Use the formula for cox(2x): cos(2x)=cos(x+x)=cos^2(x)-s...

CW
Answered by Chloe W. Maths tutor
8111 Views

A curve has equation y = 2x^5 + 5x^4 1 . (a) Find: (i) dy/ dx [2 marks] (ii) d^2y/ dx^2 (b) The point on the curve where x ¼ 1 is P. (i) Determine whether y is increasing or decreasing at P, giving a reason for your answer.

a.) dy/dx+10x^4+20x^3

d^2y/dx^2=40x^3+60x^2

b.)sub in x=-1 to dy/dx=10(-1)^4+20(-1)^3

=-10

therefore, decreasing

AF
Answered by Alexandra F. Maths tutor
9148 Views

Explain the Chain Rule

The chain rule is used to differentiate composite functions, ie "a function of a function". In this case we have an outer function and an inner function. For example

Differentia...

AC
Answered by Alex C. Maths tutor
3833 Views

What is the angle between the position vectors a and b, where a = (6i - j + 3k) and b = (-4i + 2j + 10k)?

cos(AOB) = a.b/(|a| x |b|)

a.b = (6i - j + 3k).(-4i + 2j + 10k)

      = (6 x -4...

DH
Answered by David H. Maths tutor
5722 Views

Simplify (5-root3)/(5+root3)

multiply with conjugate 5-root3 such that the denominator gets rational 

(5-root3)^2/((5+root3)(5-root3)) = (25-10root3+3)/(25-3)=(28-10root3)/22 = 14/11 - 5root3/11

EG
Answered by Evita G. Maths tutor
13145 Views

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