Solutions to Exam 1 Ma123 (Blue version), F07

Calculus (With Analytic Geometry)(8th edition)

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

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

View Full Document Right Arrow Icon
Image of page 4
Image of page 5

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

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 123 Calculus I Name: §OLUT70N§ “ BLUE. Exam I Fall 2007 RWJ No calculators allowed, one page of notes allowed Instructions: 0 Read questions carefully 0 Help me award you (partial) credit by showing your work (except on problems 4 and 5) 0 Note point values on questions — I 05 points are listed, 1 00 points is possible 0 Check your answers if you finish early 0 The exam ends promptly at 2:52 0 Good luck! 1. / 15 2. / 28 3. / 20 4 / 10 5 . / 8 6. / 9 7. / 15 /105 l. (15 pts.) The position of an object at time x is given by f(x)=\/x+l a. Find the position of the object at time x = 0. Also find the position of the object at time x28. nC/o)=J\—=[y «9/804?— =(3) b. What is the average velocity of the object over the time interval [0, 8]? 41/9} We) 3:: l c ’ ‘- Q '0 87,0 0. Give an expression for the average velocit over the time interval [x, x + h]. ’P/X*L)'L(x) - J 7(4'L\*I - x44 ’ (1. Using your answer from part c (and not any “shortcut” methods) determine the instantaneous velocity of the object at time x. \jxvrh’rf ’ MI mel JrJ'xH _______________________. In J‘kafl l'\j7<+l Qwhqto-un) ; \ ______’.__————————— In 4—5:) {\l'wa] 4—5;?) 4A fi/xru)- fi/x) __ A J , fl; k (m MEI) @‘ 2. (28 pts.) Compute the derivatives of the following. Don ’t waste time simplifying. a. 3x7 —6x3 +5x—10 " lgx?’* 5 b. (2x6 +5x4 +3x2 —x+7)sinx (/276‘4' Zoxat’éx—(D 9&1: +— (ZxékE'qu— hm'xr7> WX 13x5—4x3+3x+1 x3+2x—7 (45%+— /’2_ 'x" #3) {763+1x—7) ——(/37(5— f‘x3+3x%t)(3x"+z) _//_—__—_’__________________—_ (W3 f'Zx—7)L C. d. tan[(5x2 + 3x +1)“2] .vI/l %z[(5xzf3X+l)btj - 2%(5’X14-37fi4'l) (/ox4-3) 3. (20 pts.) Find Don ’t waste time simplifizing. X x3 sin x a. y= x2+x+3 (aklfiixk kgmvc)('x7’+‘x+})— 6(3fix)(7.7cfl) 4% (>9 ,L x*3)L b. y = (6x3 + 5x+8)10(3x2 + 2x+1)8 4%: ; /0(6x34’5ka)q(/9x"/'5) [3x7'4—1x4rl): 7" [Afirhkflw 5’(3«14—1x4—1)7 (4x44) dy 0. xy2 = sin(xy) (your expression for d— will be in terms of both x and y) x ,4— (‘PC 1 ’— ;- EI'LC 1047 47c ’7 ) x U) 7" Ir X g— (o‘) - mew) - :1: (my) Ax Jx Ax ' 1207 _. xm[¢7) 4. (10 pts.) For each of the following indicate Whether the statement is true or false (no work necessary): a. If f is continuous at x, then f is differentiable at x. True oircle one)? b. If f is not continuous at x, then f is not differentiable at x. or False (circle one)? c. For any function f, lim f (x) = f (0). True o(circle one)? d. If f and g are differentiable, then (fg)' = f ' g'. True ocircle one)? e. If f and g are differentiable, then (f + g) '= f '+ g' @ or False (circle one)? 5. (8 pts.) Fill-in the blank: a. If f '(x) exists, then we say that f is '1‘ M'b £6 at x. b. If 1imf(x) = f(c), then we say that fis mfihuws at c. X—)C 6. (9 pts.) Suppose f is a continuous flinction on [1,5]. Also suppose f(1) =—4 f(5) = 6 a. f necessarily has a zero (or root) between what two x values? [+5 b. If the bisection method is used, at what x value do we now evaluate f? 0. Suppose f is negative at the x value you gave in part b. Where do you now evaluate f? 7. (15 pts.) For the following limit problems: 0 If the limit exists, give me the (finite) value of the limit 0 If a limit does not exist, answer using 00 or —oo when appropriate, otherwise write “Does Not Exist” a.lim "2—3 z A, x.) -. A “J‘— -— .L H3" ‘9 >993 Q‘JX’V’” xa} Qua) é x2+2x—l _ (1)1440) —I [*4 b. lim H1 x + 4 H MD" ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern