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Sol-165E1-F2009

# Sol-165E1-F2009 - MA 165 EXAM 1 Fall 2009 Page 1/4 NAME:3...

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Unformatted text preview: MA 165 EXAM 1 Fall 2009 Page 1/4 NAME (:3 PM I?!) l W 1:7 M V STUDENTID RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1. 9° Write your name, 10—digit PUID, recitation instructor’s name and recitation time in 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 suﬁicient 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, calculators or any electronic devices may be used on this exam. (7) 2 . Find the domain and sketch the graph of the function 9(22) : Vac — 2. é? a. Domain: ”g. ea (g; l, . > >< 2?: 9. 123456 (a) Is the function f (:33) lniatl even, odd, or neither? gm l'ﬂ’xl :Qmﬁxi (b) Make a rough sketch of the graph of y 2 ln [ml MA 165 EXAM 1 Fall 2009 Name Page 2 / 4 2 3 (8) 3 If cos0— — ———, 7r < 6 < 1, ﬁnd the following 3 KM” [MW/W ‘ F 4‘ CW am ’6; 9:168:92??? WWX’WXW WWWW '3}, ,W 21:11:23: 1:: 2:61:23 2: (6), 4. Find all values of :1: in the interval [0, 2w] that satisfy the equation sin 2x : x/3 cos 1:. XZ‘EEJHXVR‘ (,Ocyﬁ {WWWWWWWW ﬂit/t f“ €0.ij QWMWXH hj‘uy ”1:233“ ,X‘X“ XX ““22 XXX; W ‘11 1T? 212:“ WWW \$111212? #2 W‘fF, 33W WWW ) WWX W E W W :5 33 (10) 5. If f(;23) : 2 —- 6””, ﬁnd the following: (a) A formula for the inverse function f _1(x). QWWWWX WW 5, 31 £12»? 5)? Q22) (‘2 La} WWWXWWW XXWW \é XWWX W W X‘W W 22 i Mi: 2 1 . z: :: Kmxﬁa: 9:21) XX XX) W XXXXXWX) (b) The domain of f‘l. (c) The range of f—1 kw“ (6) 6. Using a theorem about continuous functions, we can conclude that the equation 3:4 + :1: — 3— — O has a re )@in one of the following intervals. A.(1,0) B.(01) @(12) D.(2,3) E.(3,4) (a) Circle the letter of that interval H31): XX we: :99?» geﬂﬁw‘a <9] “qua-23.2%) g1)\$v14O/{XQ)W%>@ Sﬁ): ”(MPG 95(4)“; 227%} (b) State the name of the theorem you are using. I WT £1: *1“ m rid/1211M Vmﬁﬁmﬂ/ WXW 521:1: @“f‘é: ‘21 MA 165 EXAM 1 Fall 2009 Name Page 3/ 4 (12) 7. For each of the following, ﬁll in the boxes below With a ﬁnite number or one of the symbols +00, —oo, or DNE (does not exist). It is not necessary to give reasons for your answers. 2 1690; met; if? 2 _ ‘ r T (a) lim .T 2 2:1: : QAm ’X (iii-21¢ mﬁm wiggﬁ NPQ ”“2 50 *4 91.92 \$123111 1’2} 3M1; x—s—z \$1 a. 1 .2 2_\S,:t:1 (bllim —-——§= +910 m—+1(cc—1)2 (0)11m(l— 1 )2 Lam ﬁLEZt: Q1111 3* t—+0 t 3t2+t 1.413 M31211} 1—110 ta(3111-0 :3 ’1‘“ i1 :3 “£1110 32:11 4 _ (d) 113%:1: coS(\$) — m1 \$w\$%)ﬁ 1 b1; gouwsc a5x90\$ . W311 L (e) lim 6mmm —- Q W O Q 33—)(125)+ klmduw t” w» amaﬁlgyﬂ 2“”13-151’ (6) 8. Write the equations of the vertical and horizontal asymptotes, if any, of the graph of : 21: + 1. _ 3W 1:111:11 119C am a: {2:11)}??? :2 m x332, in (:1 V \$5, Vertical asymptotes i XV?!” ?1“’"Zm:5o X7321 VIP/{m 91(1) “film iii W "”2? Horizontal asymptotes “ ‘xwfﬁm >112? ymaiw .111 a? 1332 is all all L 1:: 2, l E) a: + 1 if :6 < 0 (6) 9. Find the numbers at which f (m) = 6”” if 0 g a; g 1 is discontinuous. l 2 — a: if (I: > 1 F 2: “ g 1/7 (Lamﬁi 111111153111 " View (1 ill) 21\$ A?1'1117(1,{§2l if” ,1 11221? 1.? (Fiji 3%: Z3 ’3 gr?) ‘, Qjm \$19121) Kim \$111114 -L £4111 Mi“): 1.? R57) 1 X11307 ymO‘l’ 1“ 13131 (hi R1111 its) :6 rim 1(1) 1% W: 1:11 Tl oi :11 , ;a}{ WWW X m!) it” ”4 (3‘1? ilk 1“ mm g???) D W E: 11: 11 1 g 1}; Cbéi‘crntﬁjw r MA 165 EXAM 1 Fall 2009 ' Name Page 4/4 (10) 10. Find the derivative of the function f (:13) = V 1 — 3: using the deﬁnition of the derivative ., _. f(rI:+h) —f(33) f (a?) — hm ——————— h 0 h . (0 credit for using a formula for the derivative). % (x): Oj‘m ffﬁﬁhﬁwﬁkjw :: i1 “”50 is; m waft i“)? FM 7“ ‘1 {l >‘ «’1th WW @Aﬁxfr”'i‘;j WW I” omt'fsgi'oh :4 Kim i) F?) O [4 “‘50 (6) 11. Find an equation of the tangent line to the curve y : a; + cos x at the point (0,1). :4: ”” ’i .4 1' M We ‘ :: {gt 2‘34 :4 45 4 ,1 .5, 4 (4 4) x4 >< 4 I Cl. 44 are Q (16) 12. Find the derivatives of the following functions. Do not simplify. (a) f(\$) = 36" — 3/937 17 ° 244 4 : ﬁexﬂm % 5" l 7% V ‘5- § r4) 4 z: :5 sin a: (b) y = em a» ‘ {Mgarwﬂ w 5‘ “X pr :;»’I 2% \$2.“: 696% ff: (c) h(6) z csc 0 + 66 cot 0. I fl 4 2.” 46‘ ”E “n hlhkrwcsrgcﬁtﬁ :44; 4444 €35 “i” {1* “‘6‘ (d) f(t) = x/E + t3 tan t. 4, <3 3:” l; ”Wt tom: / , w 4 F §(f):%t ‘5; 4;:‘4144 ”if ”Li/lentil“ ...
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