New User Special Price Expires in

Let's log you in.

Sign in with Facebook


Don't have a StudySoup account? Create one here!


Create a StudySoup account

Be part of our community, it's free to join!

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

Calculus Several Variables Study Guide

by: Avid Notetaker

Calculus Several Variables Study Guide Math 010A

Marketplace > University of California Riverside > Mathematics (M) > Math 010A > Calculus Several Variables Study Guide
Avid Notetaker
GPA 4.0

Preview These Notes for FREE

Get a free preview of these Notes, just enter your email below.

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

Good luck on the final!
Calculus:Several Variables
Meng Zhu
Study Guide
Calculus, Series, study, guide
50 ?




Popular in Calculus:Several Variables

Popular in Mathematics (M)

This 1 page Study Guide was uploaded by Avid Notetaker on Thursday April 21, 2016. The Study Guide belongs to Math 010A at University of California Riverside taught by Meng Zhu in Winter 2016. Since its upload, it has received 24 views. For similar materials see Calculus:Several Variables in Mathematics (M) at University of California Riverside.

Similar to Math 010A at UCR

Popular in Mathematics (M)


Reviews for Calculus Several Variables Study Guide


Report this Material


What is Karma?


Karma is the currency of StudySoup.

You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 04/21/16
  NAME CONVERGENCE TESTS FOR INFINITE SERIES  COMMENTS  STATEMENT   Geometric series       ! ar k  =  1    , if –1 < r < 1 Geometric series converges if    and diverges otherwise –1 < r < 1   Divergence test  – r   If    p    If  lim a k= 0, !a  kay or may not converge.  (nth Term test) lim ak " 0, then !a  kiverges.    !  k  !      Integr If p is a real constant, the series ! 1   =    +    + . . . +    + . . .  – series a p p p p converges if p > 1 and diverges if 0 < p # 1.  !a  has positive terms, let f(x)  b   as  tnhcitens aht ns fu(lis heeans yk  tios  integrate.  This  k e p$l a beyn  in the formula for u . kIf is decreasing and continuous for   !a 1%     Comparison test (Direct)  test only applies to series with positive terms.  bok acdn vfe(g)e  doxr   bo th diverge.  If !a k  and !b k are series   itshehsisivset  ta s ssute hratt ache trm stnr !eak ften  i le) sihae "itisg cgesrpes"d i!nbg term in !bk, then          series" !a k converges, then the "smaller  easier to apply.  This test only applies to series        Limit Comparison test   (b) if the "smkller verieess". !a with positive terms.       series" !b k diverges, then the "bigger  diverges. k  If !a     k  and !b  kre series with positive terms su c  h   Tthhaits  is easier to apply than the comparison test,    if L > 0, =e n  then both series converge or both diverge. k  ! b   k but still requires some skill in choosing the     Ratio test  if L = 0, and  series !b  kor comparison.    if L = +% a!nbdk! bconverges, then !a  konverges. k diverges, then !a  dkverges.  If !a    k  is a series with positive term s  srch t hti st when a lim ak+1  powers. k involves factorials or k th      Root test k he! ifaL < 1  t ,e series converges    k  if L > 1 or L = +%, the series diverges   if L = 1, another test must be used.  If !a    k  is a series with positive term s   ucry  hist  test when a   if L < 1a te  s eries (a )erge s=  L, then     ! k  k  ! k       Alternating Series test k involves k th powers.  if L > 1 or L = +%, the series diverges   if L = 1, another test must be used.  The series        a  Alternating Series Estimation Theor  eIm f t:he alternating series  ! (   conv er agif  a  – a  + . . .      and      –a  + a  – a  + a  – . . .  k+1 1 2 3 4 1 2 3 4  converges, then the truncat– io1n) errk ar for the n  partial sum is less than a th   (1)   a   if an alternating series cn+1 , e e.s, then the error   (Leibniz's Theorem)   The 1eri e2s  d3i vaer > . . . and     (2)  ak  =  0     ! in estimating the sum using      Absolute Convergence and   terms is less than the n+1  term. ges if   lim ak  "  0  k  !  If !a       ik ! |ias a series with nzeortoe  tt sih asrioe ceogese,tes na:bsolutely, then it   if |aerges, i.e.     | converges, then !a  converges.      if !ka | converges, then !a kconverges absolutely. k k Conditional Convergence   Otherwikse,i arges, then !a  konverges conditionally. diverges. k 


Buy Material

Are you sure you want to buy this material for

50 Karma

Buy Material

BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.


You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

Why people love StudySoup

Bentley McCaw University of Florida

"I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

Allison Fischer University of Alabama

"I signed up to be an Elite Notetaker with 2 of my sorority sisters this semester. We just posted our notes weekly and were each making over $600 per month. I LOVE StudySoup!"

Steve Martinelli UC Los Angeles

"There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

Parker Thompson 500 Startups

"It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

Become an Elite Notetaker and start selling your notes online!

Refund Policy


All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email


StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here:

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.