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Because we have a product of two functions of x, our first instinct is to apply integration by parts. Let u = e^(2x) and v' = cos(x). We then integrate v' to find v = sin(x) and differentiate u to find u' = ...

The first step in finding any turning point is to differentiate. To do this, we muiltiply x by its power and drop the power by 1. so in this senario we multiply the -2x by 2 giving us -4x and the power becom...

First take the general form of a quadratic equation, ax^2+bx+c=0, this can be written in completed square form, (x+b/2a)^2-(b/2a)^2+c/a=0, rearranging gives, x=-b/2a +/-(b^2/4a^2-c/a)^1/2, which can be writt...

(a) (i) Use the Factor Theorem to show that x + 3 is a factor of p(x). The Factor Theorem is derived from the remainder theorem. We know from the remainder theorem that by doing p(x)/(x – a) then we get a re...

There are two different methods of solving this equation and it is important to find the method that you find easiest. The first method is to split up the numbers and the letters on both sides of the equatio...