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a151q3wi - Give your answer in its simplest form d 4 dx...

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MATH 151 Answers to Assignment 3 Autumn 2009 1. Find the indicated derivative. You need not simplify your answer. (i) d dx ± x 4 + 10 5 x 3 - sec x ² . d dx ³ x 4 + 10 x 3 / 5 - sec x ´ . Answer : 4 x 3 +6 x - 2 / 5 - tan x sec x (ii) d dx ( e x cos x ). Answer : e x cos x - e x sin x 2. Find f ± ( π/ 2) where f is the function f ( x )= x sin x cos x . f ± = 1 sin x cos x + x cos x cos x + x sin x ( - sin x ). f ± ( π/ 2) = 1 · 1 · 0+ π 2 · 0 · 0 - π 2 ·· 1. Answer : - π/ 2 3. Find the tangent to the graph of y = 3 x 2 x 3 +2 at (2 , 6 / 5). y ± = 6 x ( x 3 + 2) - 3 x 2 (3 x 2 ) ( x 3 + 2) 2 . y ± (2) = 6 · 2 · (2 3 + 2) - 3 · 2 2 · 3 · 2 2 (2 3 + 2) 2 = - 6 25 . Answer : y - 6 5 = - 6 25 ( x - 2) or 6 x + 25 y = 42 4. Find d 4 dx 4 µ 16 x 5
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Unformatted text preview: . Give your answer in its simplest form. d 4 dx 4 (16 x-5 / 2 ) = d 3 dx 3 · 16 ·-5 2 x-7 / 2 ¸ = d 3 dx 3 ±-40 x-7 / 2 ² = d 2 dx 2 ·-40 ·-7 2 x-9 / 2 ¸ = d 2 dx 2 ± 140 x-9 / 2 ² = d dx · 140 ·-9 2 x-11 / 2 ¸ = d dx ±-630 x-11 / 2 ² =-630-11 2 x-13 / 2 Answer : 3465 x-13 / 2 end Typeset using A M S-T E X....
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