Calc 2 final

Question 1

For a given sequence how to determine if convergent or divergent

Answer 1

limit dne = divergent
limit exists then convergent

Question 2

What is the formula for telescoping series and how to find the sum

Answer 2

sum of (f(n)- f(n+1))
find the partial sum sn by finding n=starting term and k=n-1 and k=2
then find the formula for sn
take the limit as n approaches infinity for sum

Question 3

formula for geometric series and rules for convergence
how to find sum

Answer 3

sum of a*r^n-1 or ar^n
converges when r is between -1 and 1
divergent when greater than or equal to 1
sum is a/1-r

Question 4

Formula for alternating series and rules of convergence

Answer 4

(-1)^n-1 * an or sum of (-1)^k
if an+1 is less than or equal to an
and lim an=0 then the series converges

Question 5

ratio test vs root test

Question 6

divergence test

Question 7

p series

Question 8

integral test

Question 9

comparison test vs limit comparison tes

Question 10

absolute convergence

Question 11

Integration by parts

Answer 11

u*v * integral of v

Question 12

trigonometric integrals sin and cos

Answer 12

if power of sin is odd keep 1 din and use pythagorean theorem sin2x+1-cos2x
if cos is odd then use cos2x=1-sin2x
If both even use half angle
sin2x=1/2(1-cos2x)

Question 13

trig integrals tan and sec

Answer 13

if tan is odd keep 1 factor of tanxsecx and use tan2x=sec2x-1
if sec is even strip off sec2x and use sec2x=1+tan2x

Question 14

integration by partial fractions

Question 15

improper integrals

Question 16

sum for k
sum for k2
sum for k3

Question 17

area under curve steps

Answer 17

b-a/n
find xk= a+k times delta x
find the sum of f(xk) times delta x
then take the lim of the sum

Question 18

area between curves formula and steps

Answer 18

integral from a to b of f(x)-g(x)dx

Question 19

disk vs washer method