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Unformatted text preview: f ( x ) = (1-cos x ) 2 x , x 6 = 0 , x = 0 Show that f is dierentiable for all x , and nd 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 dierentiable at x = 1. 3. Find all points on the curve y = 2 sec x + tan x , for 0 x 2 , 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 = 3 . Use exact values....
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This note was uploaded on 11/30/2010 for the course M 408c taught by Professor Mcadam during the Spring '06 term at University of Texas at Austin.
- Spring '06