165E1-F2009 - MA 165 EXAM 1 Fall 2009 Page 1/4 NAME...

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Unformatted text preview: MA 165 EXAM 1 Fall 2009 Page 1/4 NAME " /14 STUDENT ID /30 / 24 RECITATION INSTRUCTOR Page 4 / 32 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. 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. 5. Credit for each problem is given in parentheses in the left hand margin. 6. No books, notes, calculators or any electronic devices may be used on this exam. 0.? (7) 1. Find the domain and sketch the graph of the function g(:13) : x/zr — 2. Domain : 123456 (7) 2. (a) Is the function f = ln even, odd, or neither? E: (b) Make a rough sketch of the graph of y = 1n MA 165 EXAM 1 Fall 2009 Name Page 2/4 2 (8) 3. If c0849 2 ——§, 71' < 6 < 3%, find the following: (6) 4. Find all values of w in the interval [0, 271'] that satisfy the equation sin 2x : \/§ cos 2:. (10) 5. If = 2 — em, find the following: (a) A formula for the inverse function f _1(m). (b) The domain of f—l. (c) The range of f”1 (6) 6. Using a theorem about continuous functions, we can conclude that the equation m4 + a: -— 3 = 0 has a root in one of the following intervals: A. (-1,0) B. (0,1) C. (1,2) D. (2,3) E. (3,4) (a) Circle the letter of that interval. (b) State the name of the theorem you are using. MA 165 EXAM 1 Fall 2009 Name Page 3 / 4 (12) 7. For each of the following, fill in the boxes below with a finite number or one of the symbols +00, —oo, or DNE (does not exist). It is not necessary to give reasons for your answers. mz—Za: (a) gig; $2 _4 . 2—11: (b) 333i (7:55" . 1 1 (C) i136 ("é—w +15) “ 1 . 4 _ _ (d) infirm cos($)— 1- tanm : <6) New 2 1 (f) lim 50+ 0 — m—>—5 la: + 5| — HUME (6) 8. Write the equations of the vertical and horizontal asymptotes, if any, of the graph of 2:3 + 1 y 2 :1: — 2 ' Vertical asymptotes Horizontal asymptotes a: + 1 if a: < 0 (6) 9. Find the numbers at Which = e‘” if 0 S a: S 1 is discontinuous. 2—51: if513>1 (10) (6) (16) MA 165 EXAM 1 Fall 2009 Name Page 4/4 10. Find the derivative of the function f = x/ 1 — 3: using the definition of the derivative h _ f'(a:) : lim (0 credit for using a formula for the derivative). h—>O h 11. Find an equation of the tangent line to the curve 3; = x + (3083: at the point (0,1). F—fl 12. Find the derivatives of the following functions. Do not simplify. (a) f(:1:) 2 3e” —— (c) h(6’) : csc 6 + 66 cot 6. (d) f(t) = fi+ t3 tant. ...
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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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165E1-F2009 - MA 165 EXAM 1 Fall 2009 Page 1/4 NAME...

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