{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

solutions_mid1 - MATH 2A ~ FALL 2010 First Midterm Exam...

Info icon This preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 6
Image of page 7

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

View Full Document Right Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 2A ~ FALL 2010 First Midterm Exam Version 1 Complete in pen: NAME SIGNATURE UCI ID # E—MAIL ADDRESS o This is a closed~book test. No notes, no cell phones, no graphing calculators. 0 You have 50 minutes to complete the test. o Please, write clearly and legibly, and box your answers. 0 Read all the problems first, and start with the one you find the easiest. If you have trouble with one problem, move on quickly to the next one and return to it at the end, if time permits. Write down the sequence of steps you would take to solve it, for partial credit. 0 Remember: no cheating will be tolerated! Find the following limits. ~ 3‘ 6 ~27 (a) £133 (i—35xfx-r—1) (1)) lim 2:13 32—67 7'1: QX‘M 2mg 35%”? i? ~2< Problem 1 (15 points) 2+ 52:3 “up,” 2+ E 24:23 ng}{x/W» «X45 a GM (21%» €53”? - sin 4:52) <c> gg—ér 5“” m ) Problem 2 (10 points) Decide whether the following limits exist. Motivate your answer. If the limit is equal to +00 (or ——oo), say so. (a) lim it“— 3:44 “7'4 Mg?” @513 MR (332) Problem 3 (20 points) Find the derivatives of the following functions. §Cflz 34» %’3% $243>ngfi 2% $50; 4% W; 0’) f(«77) = (860:): +1)5 Problem 4 (15 points) (23) Find the derivative of the function 33:9—32” PM 3 3C2 gm/ggw .3333: 22><\ (b) Find all points where the graph of f has a horizontal tangent. (c) Find the equation of the tangent line to the graph of f at $2: /2 fill 323 “22—\, 333 3323 333 <2 x: ’2 <2 333332§fi3 Problem 5 (10 points) Suppose that f and g are two differentiable functions and that 9(a) f (a) 9 (a) 0---- 2—H“- |: :1 Find (1) (f ~ g)’(0) We) cng + $655?» 3:503 “-1 “,192‘ ,4. X53» :3 (2) (f 09)’(2) (Sigma ML M03: Problem 6 (10 points) Let f be the function defined by: m2+1 ifxgo f($)—{2—~x ifzc>0 Decide whether the following statements are true or false. ( Briefly motivate your answer.) (a) f is continuous at 0. (b) f is continuous at 5. Problem 7 (20 points) The graph of the function f is given. Mark each of the following statements true or false. No need to justify your answer. (1) f(0) =2 {\EG (2) imf(w)=2 #63 (3) f has a jump at O. m (4) f has a removable discontinuity at 0, [1/65 (5) The limit lim f (ac) does not exist. YéS x—+ ~3 (6) The limit lim f (ac) does not exist. m $~+~3+ 7 The limit lim as does n::'\t.\\\ ( ) f( ) {mg g m—>~3— (8) fhasajump at ~3. 76“ I f» Egg 1 I; L» 3;,» :5 (9) f is continuous at a: = 44. yéfi (10) f is differentiable at a: = 4:4. ...
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