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Unformatted text preview: MAC 2311 Test Four Review, Spring 2011 Exam covers Lectures 25 – 34, except lecture 29 Online Calculus Text, Chapter 4 sec. 24 and 26 – 30, plus Chapter 5, sec. 31 – 33 omit Chapter 4, sec. 25 and 29 1. On which interval(s) is f ( x ) = 1 2 √ x 1 x 2 increasing and decreasing? Find all local extrema. 2. Find each interval on which the graph of f ( x ) = ( x 2 + 1) e x is both increasing and concave down. Find each inflection point. 3. Suppose that f ( x ) has horizontal tangent lines at x = 2, x = 1 and x = 5. If f 00 ( x ) > 0 on intervals (∞ , 0) and (2 , ∞ ) and f 00 ( x ) < 0 on the interval (0 , 2), find the xvaluse at which f ( x ) has relative extrema. Find the xvalue of each inflection point of f ( x ). Assume that f and each of its derivatives are continuous on (∞ , ∞ ). 4. Evaluate the following limits. Use L’Hospital’s Rule if it applies. a. lim x → x ln( x + 1) 1 sec2 x b. lim x → cos 2 x e x/ 3 + 1 c. lim x → 1 ln(1 x 2 ) ln(1 x ) 2 d. lim x → 1 (2 x ) tan( πx/ 2) e. lim x →∞ ( e x + x ) 1 x f. lim x → (cot x csc x ) 5. Find each horizontal asymptote of f ( x ) = x 2 e x . Use L’Hospital’s Rule if necessary. Then....
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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.
 Spring '08
 ALL
 Calculus, Geometry

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