Search over 10,000 free study notes

We must first use trigonometric identities to simplify cos²(x). We can use the formula cos(A+B) = cos(A)cos(B) - sin(A)sin(B) , where A=x and B=x, so that we ...

First we find the y coordinate which is a function of x:

x = 2+ h so  y = (2 - 2 - h)(1 + 2 + h) + 3 = -h² - 3h + 3

Now for the gradient, the line passes through points (2,3) and ...

Consider the function as 1(ln(x)) and then use integrating by parts, where you would differentiate the ln(x) part.

Formula for nth term in a geometric progression = ar^n-1

workings:  

a=12

r=1.5  because 18/12 = 1.5

Thus, using ar^n-1  -->   12 * 1.5^8 = 307.54... or 308 (to 3sf)

...

There are 2 main methods for finding a normal vector.

1. If you know two vectors that lie in the plane e.g. (a,b,c) and (d,e,f), we can find a normal vector by calculating the vector/cross p...