hw11 - Math 341 Homework 11 P131 32(b 33 35 37 P165 3 5...

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Unformatted text preview: Math 341 Homework # 11 P131. 32(b), 33, 35, 37. P165. 3, 5. P166. 8, 9. 32(b). Assume the rules for differentiating the elementary functions, and use L’Hospital’s rule and find the limit lim x → x e x- 1 . Solution: lim x → x e x- 1 = lim x → x ( e x- 1) = lim x → 1 e x = 1 . 33. Use L’Hospital’s rule to find the limit lim x → x 2 sin x sin x- x cos x . Solution: lim x → x 2 sin x sin x- x cos x = lim x → ( x 2 sin x ) (sin x- x cos x ) = lim x → 2 x sin x + x 2 cos x cos x- cos x + x sin x = lim x → 2 sin x + x cos x sin x = lim x → (2 sin x + x cos x ) (sin x ) = lim x → 2 cos x + cos x- x sin x cos x = 3 1 = 3 . 1 35. Find an equation for the line tangent to the graph of f- 1 at the point (3 , 1) if f ( x ) = x 3 + 2 x 2- x + 1. Solution: Since f ( x ) = 3 x 2 + 4 x- 1 , we get f (1) = 3 + 4- 1 = 6 . Thus, ( f- 1 ) (3) = 1 f (1) = 1 6 . The line is y- 1 = 1 6 ( x- 3) ....
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This note was uploaded on 08/13/2009 for the course MAT 371 taught by Professor Thieme during the Spring '07 term at ASU.

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hw11 - Math 341 Homework 11 P131 32(b 33 35 37 P165 3 5...

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