ma1012_hw21_201012

ma1012_hw21_201012 - ^ S AND L'HOPITAL'S RULE œ "...

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Unformatted text preview: ^ S AND L'HOPITAL'S RULE œ " 4 œ# 5x or lim xc2 x Ä 2 x c4 œ lim xc2 x Ä 2 ax c #bax b #b sin 5x Mathematics I. Homework 21: L’Hospital Rule œ lim x Ä 2 xb# " œ " 4 ¹ xœ! œ 5 or lim "0x c 3 14x xÄ0 sin 5x x lim Ä_ œ x lim Ä_ œ 3 11 œ 5 lim Part I 5x Ä 0 5x œ 5 † 1 œ 5 Thomas’ Calculus 11th Edition: Chapter 4, Section 6: 1, 2, 4, 5, 7, 9, 11, 19, 23, and 24 5c 3 10 5 5x c3x 5 x 14 œ 7 or x lim Ä_ 7x b1 œ x lim Ä_ 7b x œ 7 3x lim x Ä 1 12x c 1 Part II: Find the following limits (7.4): 1 c bax c /(1− x ) or 91. limxcx1 3 œ lim aaxxc ""ba4x2b x b+"3bb lim 4x x c + 4x + x Ä 1 →1 x xÄ1 93. lim (ln x ) x→∞ 1/ x Ä! im sin x 2x € œ lim sin x sin x € " ”ˆ x ‰ˆ x ‰ˆ " b cos x ‰• œ xÄ! cos x 2 95. lim+ x −1 / ln x x→0 x→∞ " # œ " or lim 1ccos x œ lim l 1! ) 97. # im x(Ä+ 2 xx 1 /( 2 ln x )x Ä 1 ” a" c cos xb ˆ " b cos x ‰ x2 " b cos x • € ȹ 1 ȹ x 100. lim+ ȹ 1 + ȹ x → 0 ȹ x Ⱥ x lim xÄ_ 0 œ 2 c" %x b 3 $x b " € lim % œ ! or lim #x b 3x œ lim œ x Ä _ otal: 15 x Ä _ x b x b 1 x Ä _ T 'x problems. b x 3 x "b b œ x ! " œ! € œ c2 Answers Part I: Section 4.6 1. ¼ 2. 5 4. 3/11 5x sin . ½ " c4 cos 2x œ c4(c1) œ 7. 0 9. 1 È# # x " " œ" œ lim x Ä 1 Î2 œ È# # c cos x c2 sin 2x " 4 cos x b sin x " b sin x " œc È$ # 11. 19. -5/3 23. -½ 24. 1 Part II: 91. 1/e 93. 1 95. 1/e 97. e1 / 2 100. 1 œ È# € fpm@itesm.mx ...
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