Midterm2009 - is discontinuous at x = 0 . 3. Use the...

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Calculus I - Fall 2009 Midterm Exam, October 14, 2009 In the following problems you are required to show all your work and provide the necessary explana- tions everywhere to get full credit. 1. For each of the following, decide if the limit exists. If it does, ±nd the limit. If it does not, decide also if the limit is , -∞ , or neither. (a) lim x →− 2 x 3 - 4 x 2 + x - 1 (b) lim x 3 x 2 + 2 x - 15 x 2 - x - 6 (c) lim x 3 x - 3 x - 3
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(d) lim x 0 ( x 4 - 5 x ) cos x tan x (e) lim x →∞ cos x (f) lim x →∞ 8 x 3 - x + 2 1 - 4 x 3 (g) lim x →− 1 1 x + 1 (h) lim x →− 1 - 1 x + 1
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2. Use limits to explain why the function f ( x ) = sin x if x 0 cos x if x >
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Unformatted text preview: is discontinuous at x = 0 . 3. Use the deFnition of the derivative to Fnd f ( x ) = 1 x . 4. Find an equation of the tangent and normal lines to the curve f ( x ) = x sin x at the point p 6 , 12 P . 5. Let f ( x ) = x x + x 5 . Find f ( x ) and f ( x ) . 6. Let f ( x ) = x 2-1 sec x + 3 . Find f ( x ) . 7. Match the graph of each function in (a) - (d) with the graph of its derivative in I-IV. (a) (b) (c) (d) (I) (II) (III) (IV) ANSWER: (a) (b) (c) (d)...
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Midterm2009 - is discontinuous at x = 0 . 3. Use the...

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