integration by parts

lennykravitz

hey anyone have a solution for the 2000 question 8?????

i'm trying to rape paper 2 material here to make up for my pathetic attempt at paper 1:eek:

Lucas10101

lennykravitz wrote:

hey anyone have a solution for the 2000 question 8?????

8
(A)

Ratio Test Question: Showing it's Divergent >1 for all values.

(n+2)!/2^n+2

Un => (n+2)!/2^n+2

Un+1 => (n+3)!/2^n+3

Un+1/Un => (n+3)!/2^n+3 * 2^n+2/(n+2)!

(n+3)(n+2)!/2^n.2^3 * 2^n.2^2/(n+2)!
Cancel the (n+2)! and the 2^n.

(n+3)4/8

=> 4n +12/8

lim 4n/n + 12/n divided by 8/n =>4

4>0 Implies it's Divergent.

I know it looks messy but write it down normally and it looks okay.

JC 2K3

int((e^2x)cosx.dx

u = cosx
du = -sinx.dx
v = (e^2x)/2
dv = e^2x.dx

int((e^2x)cosx.dx = cosx(e^2x)/2 + int((e^2x)sinx.dx

int((e^2x)sinx.dx

u = sinx
du = cosx.dx
v = (e^2x)/2
dv = e^2x.dx


int((e^2x)sinx.dx = sinx(e^2x)/2 - int((e^2x)cosx.dx

int((e^2x)cosx.dx = cosx(e^2x)/2 + sinx(e^2x)/2 - int((e^2x)cosx.dx
2(int((e^2x)cosx.dx) = cosx(e^2x)/2 + sinx(e^2x)/2
int((e^2x)cosx.dx = cosx(e^2x)/4 + sinx(e^2x)/4

You need part 2?

JC 2K3

@Lucas

It's always a good idea to read the title of a thread

Lucas10101

lennykravitz wrote:

hey anyone have a solution for the 2000 question 8?????

Integration by Parts

It's example 6 on the Text and Texts Book Integration by Parts section.