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## Calculus

by: Otilia Murray I

55

0

5

# Calculus MAT 021C

Otilia Murray I
UCD
GPA 3.88

Staff

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COURSE
PROF.
Staff
TYPE
Class Notes
PAGES
5
WORDS
KARMA
25 ?

## Popular in Mathematics (M)

This 5 page Class Notes was uploaded by Otilia Murray I on Tuesday September 8, 2015. The Class Notes belongs to MAT 021C at University of California - Davis taught by Staff in Fall. Since its upload, it has received 55 views. For similar materials see /class/187409/mat-021c-university-of-california-davis in Mathematics (M) at University of California - Davis.

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Date Created: 09/08/15
Math 21C Kouba The Comparison Tests and Limit Comparison Tests COMPARISON TESTS Assume that sequences an and bn satisfy 0 s an 3 bn The following statements can now be made 00 00 I If the series 2 bn converges then the series 2 an converges n1 n1 00 00 II If the series 2 an diverges then the series 2 bn diverges n1 n1 LIMIT COMPARISON TESTS Assume that we know what the series 2 bn does n1 0 converge or diverge and we are trying to determine what the series 2 an does Assume n1 a also that an gt 0 bn gt 0 and lim 52 L Where L is a posztwe nite number 71 00 n 00 00 I If the series 2 bn converges then the series 2 an converges n1 n1 00 00 II If the series 2 bn diverges then the series 2 an diverges n1 n1 THE FOLLOWING ARE SPECIAL CASES FOR THE LIMIT COMPARISON TEST 00 00 III a If L O and the series 2 bn converges then the series 2 an converges n1 n1 00 b If L 0 and the series 2b diverges then NO CONCLUSION can be m n1 made about the series 2 an using this test 111 00 00 IV a If L 00 and the series 2 bn diverges then the series Z an cdiverges n1 n1 00 b If L 00 and the series 2 bn converges then NO CONCLUSION can be m n1 made about the series 2 an using this test n1 Maw am 11 1M SMLWWDW JWCVWw Jr ea M Ohio W400 CO Z a a alaampam x Q 2 WIZO 0 Z W 1vrv3v 1 x gn tltwltl 0 k Y who WWmew m n1 WWW IV v vm 2pr W vii 3JV39MW1TJLQJW Na K I 3 i I H m p A 3 hp 5 4 WW pRM WMzamp J o X31 J M amp W MW g tcwjz OhC22C32m a C11 S 4LX97 W Mm 199001a3 fw7lt WW 7 W W 142 R CWI 9CM2PV3 TM 5094CX0LgtLlt Rn lt W CXJM 5 w ww W quot 00 q 44anam 24 1 9 3 V I OK W a a be Ana Hz b 69 M s WMW W n90 anLQWMWM M anzo 1quot Jam NW W409 00 n W 61 4 ao aala3 aqm1an VO 4quot 41 4 K Cl an 60 QVH K TM lt an M 61 a ala3qnu J w1 M 5 DQQSIQWJWJ W39v qm to gt0 4 a ql ahant W M v1 4W4 1 L M oo lat1 a LltlWV2TQM Lgtljgt kM 4 0LZIJ7EMMWW 11 3 QW7QLJL 41 41al43quot39 4 4 4 f AAA lt9 XII V1 pm OM L L4lt 7BL IV am BM L b Wl qw W CgtLZIJWMWJCQW W

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