2008_05_30_13_52_17

2008_05_30_13_52_17 - Midterm 1. \Vinter 2003. Math 20A Wt...

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Unformatted text preview: Midterm 1. \Vinter 2003. Math 20A Wt 7) 1-w- H -t.*/ CIRCLE THE SECTION IN “’l-llCl-I YOU ARE A'I‘TENIHNG: .401 A02 A03 A04 AOS A (1,. A07 A08 1 m 2 m 3 m 4 1n 5 m 6 1m 7 ll] 8 1m P P g P P . . P i . . P i . Ben Mike .I o h n A n no I Be sure to show your work. No credit will be given for unsupported answers. lfa problem statement asks you to provide a solution using a certain method, then you will not receive credit for doing a problem by a different method. As promised. here are some theorems and definitions. You may or may not need these. THE SQUEEZE THEOREM Assume that for x i r (in some open interval containing c'}. f(.\') S {(I) S “(3') and limflx) : lim “(.1') = L . Then lint ft 1:} exists and lint/Ix) = L. I )t' \ Dt \' n' THE INTERMEDIATE VALUE THEOREM It“ [(35) is continuous on a closed interval [n.h] and flu] i fut) . then for every value M between/(a) and jib). there exists at least one value (' e (u.h} such that f((') = M. f'tu) = “mm b 'u h dfl/Vl\flb{h f r.___‘ (f (T 1. (10 pts) Let ./'(.\')= «1.13 +4. ‘ Wilt [ Wan w? 39th“; So datum/{1x o L $00: sbngs%;¢¢l ail Y\MJQ66 CLM-mu'w =» \Afj—q T 0 96$?le xa—Hf i. o XZ+WZ¢O \uywlh‘* J OLLnanh 3:..— W1 m (21) Find the domain and range of]: (b) Find a formula for f'l{x). 33(M2m ‘—-.——-.--—-u—— VLVXB—N g Pm -: mailbag ?' Yl;_x3+gflfl_ 2. (15 pts) Solve the following equations forx. Your answer needs to be simplified as much as possible in order for you to receive full credit for this problem. 3. (10 pts) Use the Intermediate Value Theorem to determine whether the equation cos(2x) = sin 3: 72' has any solutions on the interval [03—]. Be sure to justify your answer. 4 (a “119' O)-——(9‘(¢J {It Cost“... Ar” \ (“l-'2" 3“} 2. '. T (1.51 $016) g”‘<"fl*”?i<%) -.—_ r2; _. a 7.- JEN?) '1' ":5 5’ "C051 are, cm fiber/[5 21 4-—--tu. Vat/«has. 1R0 71*) (Hay-:4 é£(_"§):\E-,\ 4%er a 4. (15 pts) (a) Compute the derivative of _/'(.\') = .1'3 at .r = 4 using the limit definition. Simplify your answer as much as possible. [I‘m iththfi «— £090 7 in.“ i: QLHh) _. £04) w H two ———————~———-—-— h 2 “m (“JrhiL-“W :iim Mist/1+le kflbo h V1170 I" "3 I‘WMCBW') :Bm: ~t>o “‘T k (b) Find an equation of the tangent line to the graph of j'(x) = x2 at (4, I6). £100 32% smamzzx :__@=<~F’(01) 3—- £(u.\:1”~’(oi) (Xflcq «Emir—flopficq) Y‘lkpr— éme-Wi g Y :91 _,, gage—“fl (c) Find the average rate of change off with respect to x over the interval [3, 9]. DO NOT simplify " m -— 'm ) hi1?!» - q R 0 7:: HM h: #- 42(2)) - "DO : ’1'“ 1 (5+ —-—- Ci *2. + )0) a: it-Do X _5 ...
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This note was uploaded on 12/02/2009 for the course BILD BILD 3 taught by Professor Woodruff during the Fall '08 term at UCSD.

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2008_05_30_13_52_17 - Midterm 1. \Vinter 2003. Math 20A Wt...

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