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Unformatted text preview: at each point of discontinuity to justify your conclusions. f ( x ) = x 2-4 x + 4 | x 2-3 x + 2 | , x sin x, x < 2. Use the denition of derivative to calculate f ( x ) for f ( x ) = 2 x + 5. 3. Show that the graph of the function f ( x ) = 2 cos x-x 2 crosses the x axis. Approximate the x-intercept with one decimal place accuracy. (In other words, the dierence between your approximation and the actual intercept must be less than 0.05). 4. Let g ( x ) = x 2 5 . (a) Is g continuous at x = 0? Use the denition of continuity to justify your answer. (b) Is g dierentiable at x = 0? Use the denition of dierentiablity to justify your answer. 5. Let f ( x ) = x 1 3 1 + cos 1 x . Does lim x f ( x ) exist? Is f continuous at x = 0? Is f dierentiable at 0? Justify your answers....
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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