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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$l MA 165 EXAM 1 Fall 2006 Page 2/4 1
(6) 3. If cosB 2 —5 and 7r < 9 < 3%, ﬁnd the following: (6) 4. Solve the equation 35c + Zlcc — 3] = 7. (6) 5. Find the equations of the vertical and horizontal asymptotes of the function
1 ~ 256 f($)_ 5646. 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;:
VIECL, 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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 Fall '08
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 Calculus, Geometry, Derivative, Continuous function, Limit of a function

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