165E3-F2006 - MA 165 EXAM 3 Fall 2006 Page 1/4 NAME...

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Unformatted text preview: MA 165 EXAM 3 Fall 2006 Page 1/4 NAME 10—digit PUID RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1. Write your name, 10—digit PUID, recitation instructor’s name and recitation time in the space provided above. Also write your name at the top of pages 2, 3 and 4. 2. The test has four (4) pages, including this one. Write your answers in the boxes provided. 4. You must show sufficient work to justify all answers unless otherwise stated in the problem. Correct answers with inconsistent work may not be given credit. Please write neatly. Remember, if we cannot read your work and follow it logically, you may receive no credit. 5. Credit for each problem is given in parentheses in the left hand margin. 6. No books, notes, calculators or any electronic device may be used on this exam. 9° (10) 1. Find the absolute maximum and absolute minimum values of the function f(x) = x3 — 121: + 1 on the interval [0,3]. abs. max. f( )= abs. min. f( )= (10) 2. Suppose f is continuous on the closed interval [2, 5] and differentiable on the open interval (2,5). (i) Complete the following statement, and give the name of the theorem used: Statement: There exists c in the interval (2, 5) such that f ’ (c) 2 Name of theorem used: (ii) Suppose f’ 2 2 for all x on the open interval (2, 5). Find the smallest possible value for f(5) when f(2) : 4. HI MA 165 EXAM 3 Fall 2006 Page 2/4 Name: 6 (10) 3. The only critical numbers for a continuous function y = f defin‘d on the interval (~3, 3) are —2 and 0. We know that >0 if—3<x<~2 f’(zv) <0 if—2<x<0 <0 if0<cc<3. Determine whether f (—2) and f (0) are local maximum, local minimum or neither. f(—2) is f([)) IS (20) 4. Find each of the following as a real number, +00, —00 or write DNE (does not exist). (a) lim COSIL' m—>(7r/2)+ 1 — sina; (b) lim (—L “ 1 " x) m—yO 11:2 1. (c) m1)r(1)1+x(ln x) (d) lim (V332 + a: — cc) $—)OO (8) 5. Compute lim 50% I—HDO MA 165 Name: (18) 6. Let my) 2 m EXAM 3 Fall 2006 Page 3/4 + 1. Give all the requested information and sketch the graph of the function on the axes below. Give both coordinates of the intercepts, local extrema and points of inflection, and give an equation for each asymptote. Write NONE where appropriate. horizontal asymptotes :: vertical asymptotes intervals of increase intervals of decrease local minima _—_l intervals of concave down intervals of concave up points of inflection MA 165 EXAM 3 Fall 2006 Page 4/4 Name: (14) 7. Use calculus to find the largest area of a rectangle inscribed in a circle of radius 1. W3) = 7. (5) 8. Find if 3 +162“ mu) : 1 (5) 9. Find the most general antiderivative of sin a: f($) = cos2 :I: ...
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This note was uploaded on 09/14/2011 for the course MA 165 taught by Professor Bens during the Fall '08 term at Purdue University-West Lafayette.

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165E3-F2006 - MA 165 EXAM 3 Fall 2006 Page 1/4 NAME...

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