review2s11

# review2s11 - 4 3 2 1 0.5 1.0 1.5 2.0

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MAC 2311 Test Two Review, Spring 2011 Exam covers Lectures 10 { 18: Chapter 2, Section 10 { Chapter 3, Section 18 1. Evaluate each limit: a) lim x !¡1 ( x ¡ x 3 ) b) lim x ! 3 + arctan ± 4 x ¡ 3 c) lim x !¡1 p 9 x 2 ¡ 1 2 ¡ x d) lim x !1 ( e ¡ x sin x ) e) lim x ! 0 sin x ¡ x 2 x 2. Find each vertical and horizontal asymptote of the following functions: a) y = 2 x p x 2 + 1 ¡ 2 x b) f ( x ) = 2 e x 4 e x ¡ 3 3. Use the deﬂnition of derivative to ﬂnd a) d dx cos(2 x ), and b) d dx ± 4 p x . 4. Use the deﬂnition of derivative to ﬂnd f 0 ( x ) if f ( x ) = x 3 ¡ 2 x . Then ﬂnd the equation of the normal line to f ( x ) at x = 3. 5. If f ( x ) = ( 2 ¡ x j x j x < 0 2 + sin x x 0 , ﬂnd the following. For (a) and (b), use limits only. a) Is f ( x ) continuous at x = 0? b) Find f 0 (0) if possible. c) Find an expression for f 0 ( x ). d) Sketch the graph of f ( x ). 6. Indicate whether each of the following statements is true or false. a) If f is continuous at x = a , then f is diﬁerentiable at x = a . b) If f is not continuous at x = a , then f is not diﬁerentiable at x = a .

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## This note was uploaded on 05/17/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

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review2s11 - 4 3 2 1 0.5 1.0 1.5 2.0

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