Search over 10,000 free study notes

Take the example f(x)=(2x^2+1)/(3x+5) , where we're finding the gradient at x=0. First, you need to differentiate f(x) to get f'(x). Because f(x) is a fraction where both the numerator and denominator are...

Firstly you have to find the turning points of the graph. This is done by differentiating the equation of the line. Once you have found this first derivative, equate the equation to zero. Now solve the eq...

i) By integration by parts, we see that it equals (x)(e^x)-(e^x)+C, where C denotes the constant of integration. ii) (x)(y)(e^x)+C, where C denotes the constant of integration.

First, you start by replacing sin^2(x) with 1-cos^2(x) as you want the equation to be in terms of cos(x) and you know sin^2(x)+cos^2(x) = 1. Then you rearrange the equation to get 0 on one side so that yo...

x^4 -8x^2 +15 = 0, we rewrite the equation in square form as (x^2-4)^2 -16 +15 =0 (x^2 -4)^2 = 1 x^2 -4 = ±1 so x^2 = 4±1, (x^2 = 3 or x^2 = 5) Therefore x = {-√3, √3, -√5, √5)