UCR - MATH 009C - Week 3: Calculus 9C Lecture - Class Notes

View Full Material##### School: University of California Riverside

##### Department: Applied Mathematics

##### Course: First Year Calculus

##### Professor: Steven Gindi

##### Term: Spring 2019

##### Tags: Integraltest and DivergenceTest

##### Name: Week 3: Calculus 9C Lecture

##### Description: Covers convergence and divergence tests and the integral test

##### Uploaded: 04/20/2019

**3**Pages

**19**Views

**15**Unlocks

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##### School: University of California Riverside

##### Department: Applied Mathematics

##### Course: First Year Calculus

##### Professor: Steven Gindi

##### Term: Spring 2019

##### Tags: Integraltest and DivergenceTest

##### Name: Week 3: Calculus 9C Lecture

##### Description: Covers convergence and divergence tests and the integral test

##### Uploaded: 04/20/2019

**3**Pages

**19**Views

**15**Unlocks

- Better Grades Guarantee
- 24/7 Homework help
- Notes, Study Guides, Flashcards + More!

Unformatted text preview: Claim that if Iri2, then then Sn's Converge to as n + le Irici then limp !0 (like to, ie, ie it rito) Solim S lim - - Impul to Fr Example 1-t t - + - + ... Does this converge? If so, what to? This is a parete series. It's mi with LO Our theover converges to Say the riesconeiges (--) 3 since ir <1, and it 3). Convergence & Dwergence Tests when to ford out de series Converse or diverse ? we need tests Theorem 8.2.3 Simple Divergence Test if di is a sequence that does not converge to O, then ai diverses Example: 1-1+1-1+1 - ... o Where di () feta Does not curge to zero does not converge too, ai ai dierges as welve meady Seen: the partial sums dont converge 2 0 Cobre 2 + +Example: a where 1, 2, 3, ... Simple divergence This says quente converges 0, as we rething doet this. Does 2 seen the Converge? Pa sms: n fact 2 diverges. If we createn Targe crong 2 t became as large as we Tike but Every, 2 6 needs to be hige. > 5 this will be true Why does this series dirige? T V WatWVg + Vint. this V2 V2 The Sun is bigger than + 2 1 + V +..., dierges. This senes t is called a harmonie series. Themem 8.1.3 The series & coi converses it a convergess 34 they en comerge, ten care este ne conerge, ten dos tube andIf a diverges & e o then cai diverges Proof a lim 2 of first part suppose Comerges. This means exots Note: ca(ca. *ca, + ... + can) clot...tan) so by cont ca converges 50 The Integral Test The dea of this cure I shape is di since the ith rectangle has area 2 height . height yofc) The area of this shape is foldklim S fx) dx M- Thegem 8.341 The Integral Test Suppose f is a function that's non-negative : +(x) 20 for an X de cireasing: if xsy then f(x) 2 fly) Let ai * Fli) for 1.0,12,3, di coneiges if & only folds coveres. ie. tim Zaits it n-001 only v lom flax exists

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