165E1-F2006 - MA 165 EXAM 1 Fall 2006 Page 1/4 NAME/12...

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Unformatted text preview: MA 165 EXAM 1 Fall 2006 Page 1/4 NAME /12 10—digit PUID /30 /28 RECITATION INSTRUCTOR /30 - RECITATION TIME /100 DIRECTIONS 1. Write your name, 10—digit PUID, recitatiOn instructor’s name and recitation time in ewsv ()1 Q ' 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 or calculators may be used on this examf . Find a formula for the inverse of f(a:) : \/7 — 23:. f_1($)== (6) 2. Let fix) : 22: + c and g(x) : 33: + c2. Find a nonzero constant c such that (f09X$)=(90fX$l MA 165 EXAM 1 Fall 2006 Page 2/4 1 (6) 3. If cosB 2 —5 and 7r < 9 < 3%, find the following: (6) 4. Solve the equation 35c + Zlcc — 3] = 7. (6) 5. Find the equations of the vertical and horizontal asymptotes of the function 1 ~ 256 f($)_ 564-6. Vertical asymptotes Horizontal asy mptotes (6) 6. (a) Complete the definition: The function f is continuous at a if liLn II; (I (b) For what value of a is the function f continuous? f() a552, ifscgl 11;: VIE-CL, lfCC>1 . in an equatlono t etan ent me tot ecurve : cc — :ratt epom , . 6)7F'd ‘fh g 1. h y 32 5 h 't(22) MA 165 EXAM 1 Fall 2006 Page 3/4 (16) 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. (3) lim aim—2x): 1—)00 l2-$l 1—)2+ 2 —.’E . 33—2 ‘ (b) 1151311 (32—1)? —, l ll 11'} + 1:3 + 3x5 1' ———————-——— (d) $320 1— x2 + :34 (4) 9. Simplify ln(lnee). !ln(lnee) = - (4) 10. Solve ln(:1: +1)2 : 2 for x. M : 4, find lim f($) z—p2 :1:- 2 1—)2 lim f(:£) : 2—)2 MA 165 EXAM 1 Fall 2006 Page 4/4 2 +3 (0 credit for using a formula for the derivative). (10) 12. Find the derivative of the function f(x) 2 using the definition of the derivative: 2: h—)0 h (6) 13. Which of the following statements about the function 232, if —1gx<0 1, ifsz x, if0<x<1 0, if1§x<2 are true and which are false? (Circle T or F) (a) lining f(x) = o (b) lim f(x) = 1 $—)0 (c) lim f(x) = 1 T F $—)(—1)+ (4) 14. For what value(s) ofx does the graph of f(:c) : 3x2 +x+7 have a horizontal tangent? (10) 15. Find the derivatives of the following functions. (It is not necessary to simplify). (a) y = (tan x)(:1:3 + 2). 0)) f(x) = ...
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