Search over 10,000 free study notes

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 be...

(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 w...

A. t=0 ; x=250,000 B. 2020, so t=3. plug in to equation > x=250,000e^(0.012)3 = 259,163 (people so cannot round up) C. Population to double so 500,000 = 250,000e^(0.012)t -> 1/0.012(ln2) = t t= 57.7...

step 1 remember than the a and b terms locate the centre of the circle on the axis so we can substitute in the centre values for a and b. (x-5)^2 + (y-(-3))^2 = k. (x-5)^2 + (y+3)^2 = k.

Step 2. k ...