This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full 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—35xfxr—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
 Fall '10
 AlessandraPANTANO
 Calculus

Click to edit the document details