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408CF09assign3 - f x =(1-cos x 2 x x 6 = 0 x = 0 Show that...

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M408C Fall 2009 Assignment 3 Due Thursday, September 17 You should have read and understood sections 3.3, 3.4, and 3.5 before completing this assignment. You must show sufficient work in order to receive full credit for a problem. Please write legibly and label the problems clearly. Circle your answers when appropriate. Multiple papers must be stapled together. Write your name and the time of your discussion section on each page. You may use calculators for arithmetic. I strongly discourage you from using a cal- culator to do any algebraic simplification, etc., since you will not be allowed to use one on the exams. Feel free to discuss these problems with your classmates. However, each student must write up his or her own solution. 1. Let
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Unformatted text preview: f ( x ) = (1-cos x ) 2 x , x 6 = 0 , x = 0 Show that f is differentiable for all x , and find f (0). Determine whether or not f is continuous at x = 0. 2. Let f ( x ) = ( x 2-4 x + 4 , x ≥ 1 ax + b, x < 1 Find values of a and b so that f is differentiable at x = 1. 3. Find all points on the curve y = 2 sec x + tan x , for 0 ≤ x ≤ 2 π , where the tangent line is horizontal. Use exact values. 4. Find the indicated derivatives. Simplify your answers to a reasonable degree. (a) d dx q cot 2 ( x ) + x 2 (b) d 2 dx 2 [csc x ] 5. Let f ( x ) = ± sin x 1-cos x ¶ 2 . Find the equation of the tangent line to the curve y = f ( x ) when x = π 3 . Use exact values....
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