165E1-F2007

165E1-F2007 - (6 MA 165 EXAM 1 Fall 2007 Page 1/4 NAME Page...

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Unformatted text preview: (6) MA 165 EXAM 1 Fall 2007 Page 1/4 NAME Page 1 / 12 STUDENT ID Page 2 /30 Page 3 / 25 RECITATION INSTRUCTOR Page 4 / 33 RECITATION TIME TOTAL /100 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. . The test has four (4) pages, including this one. . Write your answers in the boxes provided. . 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. . Credit for each problem is given in parentheses in the left hand margin. . No books, notes, calculators or any electronic devices may be used on this exam. 2. If f(a:) : fl and 9(22) = . Find all values of :r in the interval [0, 27r] that satisfy the equation sec 1‘ = 2 sin :12. E; 1 , find the functions f o g and g o f and their domains. $— (f o 9W) ll domain : (90f)($) domain : MA 165 EXAM 1 Fall 2007 Page 2/4 (6) 3. Find a formula for the inverse of f(m) 2 2:173 + 3. (4) 4. Solve the equation 6290+3 — 7 : 0 for :13. an? if :1: S 2 ~ . . . , , find the value of the constant c for which hm f(a:) 0 ~— 51: if a: > 2 w—+2 A C‘. v C! 7. Hm) :{ exists. (1 ll (6) 6. Find the equations of the vertical and horizontal asymptotes of the graph of 11:2 + 4 2:2 — 1' y: Vertical asymptotes Horizontal asymptotes (8) 7. Find the exact numerical value of the following: (a) 621113 : —ln4) _ (c) tan(7re (d) cos(ln l) : MA 165 EXAM 1 Fall 2007 Page 3/4 (15) 8. For each of the following, fill in the boxes below with a finite number, or one of the symbols +00, ~00, or DNE (does not exist). It is not necessary to give reasons for your answers. (2 + h,)3 - 8 <2» ,l ’ : <0) $432)— H4 , 7r (d) lim 1:2 Sin ~ : m—H) j; I — 1 (e) lirn J:— : (3—H) x2(:I;+ 3) (4) 9. True or False. (Circle T or F) (a) The function f(a:) : Ia: — 1| is continuous at :2: : 1. T F (b) The function f(m) = is differentiable at a: 2 O. T F (c) The function f(a:) : is differentiable at x = —1. T F (d) The function g(:1:) = 111(33 — 1) is continuous at w = 0. T F 23: (6) 10. Find an equation of the tangent line to the curve y 2 at the point (1,1). $+1 MA 165 EXAM 1 Fall 2007 Page 4/4 1 . . (11) 11. Find the derivative of the function f : —2 using the definition of the derivative x f’ : ’lLirn) (0 credit for using a formula for the derivative). —+ (6) 12. For What values of x is the tangent line to the curve y = 3:132 — 1 parallel to the line :1: — 2y 2 —2. (16) 13. Find the derivatives of the following functions. (It is not necessary to simplify). 1 NF (a) 11:752— (b) y = (1 — e“) tanx. l 1+sin$ x+cosaf ...
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165E1-F2007 - (6 MA 165 EXAM 1 Fall 2007 Page 1/4 NAME Page...

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