Calc 2 Exam 2

Front 1

Inf

integral test

Back 1

Change to fx

must be

positive

continuous

Decreasing function

integral

Front 2

Inf

divergence test

Back 2

lim of an DNE or isn't zero

than the infinite series is divergent

Front 3

Inf

limit comperison test

Back 3

Let An and are Bn be positive

▪If lim An/Bn is positive then sum of An converges if and only if the sum of Bn converges

▪If lim An/Bn is zero and the sum of Bn converges than An converges

▪if If lim An/Bn is infinite and the sum of Bn diverges then sum of An also diverges

Front 4

Power series

Back 4

series in form

1/n^p

converges when p >1

diverges when p<1,p=1

Front 5

Integral test

Back 5

let f(x) be continuous, positive, decreasing function

1 if integral from 1 to infinity f(x)dx converges

than the infinite series converges

2 if integral from 1 to infinity f(x)dx diverges than the infinite series diverges

Front 6

geometric series form

Back 6

sum of A×R^n from 0-infinity

con |r|<1

div |r|>1,|r|=1

Front 7

p series

Back 7

sum from 1- infinity of

1/n^p

con p>1

div p<1,p=1

Front 8

harmonic series

Back 8

sum from 1- infinity of

1/n

diverges

Front 9

Sine double angle identity

Back 9

Sin(2theta)=2sin(theta)cos(theta)