HW8 - Math 191 7.6: 10 a. true; b. true; 1 x+3 1 x HW 8...

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Unformatted text preview: Math 191 7.6: 10 a. true; b. true; 1 x+3 1 x HW 8 Solutions = x x+3 < 1 if x > 1 (or sufficiently large) 1 x 1 1 x + x2 1 x =1+ < 2 if x > 1 (or sufficiently large) 1 = limx (1 - x ) = 1 c. false; limx x 1 1 x - x2 1 x d. true; 2 + cos x 3 e. true; e +x ex =1+ 3 2+cos x 2 if 2 x x ex and ex 0 as x is sufficiently large x1+ 1 x x ex < 2 if x is sufficiently large f. true; limx g. true; ln(ln x) ln x x ln x x2 ln x ln x = limx ln x x = limx 1 x 2x x2 +1 1 =0 < = 1 if x is sufficiently large = limx = limx x2 +1 2x2 h. false; limx 7.7: 4 a. c. 7.7: 6 a. b. c. 7.7: 8 a. b. c. 7.7: 10 6 ln x ln(x2 +1) = limx 1 2 + 1 2x2 = 1 2 b. - 4 3 2 3 4 5 6 4 5 6 3 a. - 4 b. 3 c. - 6 5 7.7: 14 = tan-1 ( 4 ) sin = 4 , cos = 3 , sec = 5 , csc 4 , and cot = 3 5 5 3 3 4 1 7.7: 22 tan(sec-1 1) + sin(csc-1 (-2)) = tan(cos-1 1 ) + sin(sin-1 (- 1 )) = tan(0) + sin(- ) = 0 + (- 2 ) = - 1 1 2 6 2 1 1 7.7: 24 cot(sin-1 (- 2 ) - sec-1 2) = cot(- - cos-1 ( 2 )) = cot(- - ) = cot(- ) = 0 6 6 3 2 2 y -25 7.7: 32 = sec-1 y indicates the diagram tan sec-1 y = tan = 5 5 5 7.7: 36 = tan-1 x x2 +1 indicates the diagram sin tan-1 x x2 +1 = sin = x 2x2 +1 1 y y 2 - 25 5 Figure 1: Problem 7.7: 32 2x2 + 1 x x2 + 1 Figure 2: Problem 7.7: 36 2 ...
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This note was uploaded on 06/19/2008 for the course MATH 1910 taught by Professor Berman during the Spring '07 term at Cornell University (Engineering School).

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HW8 - Math 191 7.6: 10 a. true; b. true; 1 x+3 1 x HW 8...

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