165E1-F2006

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

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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) = ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern