Download Instructor's Solutions Manual for Thomas' Calculus, by William Ardis, Maurice D. Weir PDF

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By William Ardis, Maurice D. Weir

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Read Online or Download Instructor's Solutions Manual for Thomas' Calculus, Multivariable, Twelfth Edition vol 2 PDF

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Extra resources for Instructor's Solutions Manual for Thomas' Calculus, Multivariable, Twelfth Edition vol 2

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Diverges by the Root Test: n lim an œ n lim œ n lim Ä_ Ä _ É a#n b # Ä_ n 4 œ_€1 n n anb1 an 61. converges by the Ratio Test: n lim Ä_ 1†3 â (2n c 1) (2†4 â #n) a3n b 1b 62. converges by the Ratio Test: an œ Ê n lim Ä_ (2n b 2)! d# a3nb1 b 1b # œ n lim Š 4n b 6n b 2 ‹ Ä _ 4n# b 8n b 4 63. b# a3n b 1b (2n)! œ1† " (n b 1)p † " 3 np 1 œ " 3 anb1 an œ n lim Ä_ " (ln (n b 1))p † † 1†2†3†4 â (2n c 1)(2n) (2†4 â 2n)# a3n b 1b œ œ n lim Ä_ 4n 2n n! 1†3† â †(2n c 1) œ œ n lim Ä_ 2n b " (4†#)(n b 1) (2n)!

An b 1 b2 9œ 3 2 †2 lim Š anb" b†n! † n nÄ_ 3 lim ˆ n3b n †3 † œ nÄ_ b1bc1b! b1bb1b2 c1b! 9 anb1b2 aan € 0 for all n 1; lim Œ nÄ_ aan an _ n! 2n ‹ œ _ n œ lim ˆ n b2 " ‰ œ 0  1 Ê ! 2n! converges nÄ_ 3n ‰ nb2 nb3 ‰ ˆ1‰ œ lim ˆ 3n b 6 œ lim 3 œ nÄ_ lim Š na†nanbc21b2b! † nÄ_ n œ1 nÄ_ a n b "b 2 an c 1 b ! ‹ _  1 Ê ! n 3bn 2 converges 1 3 n œ1 bn 3n b 4n b 1 œ lim Š nn2bb2n 4n b 4 ‹ œ lim Š 2n b 4 ‹ 3 2 2 nÄ_ nÄ_ c 1 b! œ lim ˆ 6n 2b 4 ‰ œ _ € 1 Ê ! aann b diverges 1 b2 nÄ_ 4. 2nb1 n†3nc1 n œ1 € 0 for all n 1; lim : nÄ_ _ 2anb1bb1 b1b†3anb1bc1 2nb1 ; n†3nc1 an nb1 lim Š anb21b†3†n2c1 †3 † œ nÄ_ n†3nc1 2nb1 ‹ œ lim ˆ 3n2nb 3 ‰ œ lim ˆ 23 ‰ œ nÄ_ nÄ_ 2 3 1 nb1 Ê !

N 2 an b 2 b ! nx32n n œ2 an € 0 for all n 1; lim : nÄ_ b 1b2aan b 1b b 2b! b 1bx32an b 1b n2 an b 2b! ; nx32n an œ b7 ˆ 6n b 15 ‰ ˆ6‰ œ lim Š 3n27nb2 15n b 18n ‹ œ lim 54n b 18 œ lim 54 œ 2 nÄ_ nÄ_ nÄ_ 2 3ban b 2b! lim Š an ban1bba1nbb † †nx32n †32 nÄ_ 1 9 _ nx32n n 2 an b 2 b ! ‹ œ lim Š n nÄ_  1 Ê ! n annx3b2n2b! converges 2 n œ1 Copyright © 2010 Pearson Education, Inc. Publishing as Addison-Wesley. 3 b 5n2 b 7n b 3 ‹ 9n3 b 9n2 598 8. Chapter 10 Infinite Sequences and Series n †5 n a2n b 3b lnan b 1b € 0 for all n 1; 1b†a2n b 3b lim Š 5an b † na2n b 5b œ nÄ_ lim Œ a2an nÄ_ lnan b 1b lnan b 2b ‹ an b 1b†5nb1 b 1b b 3b lnaan b 1b b 1b 9 n†5n a2n b 3b lnan b 1b n b 1 b† 5 † 5 lim Š a2nab 5b lnan b 2b † n œ nÄ_ a2n b 3b lnan b 1b ‹ n †5 n a b b 15 b 25 ‰ lim Š 10n 2nb2 25n † lim Š ‹ † lim Š lnlnann bb 21b ‹ œ lim ˆ 20n 4n b 5 b 5n 2 œ nÄ_ nÄ_ _ nÄ_ nÄ_ 1 nb1 1 nb2 ‹ n †5 !

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