Unformatted text preview: at each point of discontinuity to justify your conclusions. f ( x ) = x 24 x + 4  x 23 x + 2  , x ≥ sin x, x < 2. Use the deﬁnition of derivative to calculate f ( x ) for f ( x ) = √ 2 x + 5. 3. Show that the graph of the function f ( x ) = 2 cos xx 2 crosses the x axis. Approximate the xintercept with one decimal place accuracy. (In other words, the diﬀerence 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 deﬁnition of continuity to justify your answer. (b) Is g diﬀerentiable at x = 0? Use the deﬁnition of diﬀerentiablity 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 diﬀerentiable at 0? Justify your answers....
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 Spring '06
 McAdam
 Continuous function, decimal place accuracy

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