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Sol-165E1-F2008

Sol-165E1-F2008 - MA 165 EXAM 1 Fall 2008 Page 1/4 STUDENT...

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Unformatted text preview: MA 165 EXAM 1 Fall 2008 Page 1/4 STUDENT ID RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1. 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. 2. The test has four (4) pages, including this one. 3. Write your answers in the boxes provided. 4. You must show sufficient work to justify all answers unless otherwise stated in the problem. Correct answers with inconsistent work may not be given credit. 5. Credit for each problem is given in parentheses in the left hand margin. 6. N0 books, notes, calculators or any electronic devices may be used on this exam. (6) 1. Find :he domain of the function h(:c) = 47.3%. x » 5~7< > 0 C? X (x —-S) > O X(x—5) + 0 ’ O I > o 5 " ~00<x40 , .' 5‘<x<oo 6-95"? {—oo)O)U(S/OO) ._ <23 ) e E1 (8) 2. If f (as) = 1 —— 3:1: and g(a:) = cos as, find the following 2.10 am». NFC (% ° ‘3) (’0 =% (‘ifXDf'Cé-(W) =3 mew) (g o gm) = cos (mus MA 165 EXAM 1 Fall 2008 Name —_ Page 2/4 (6) 3. Find all values of a: in the interval [0, 2%] that satisfy the equation cosx + sin 2x = 0. Oo§7< + 2 sinw cosy :0 C2) (957‘ (i *2 5“”): 0 ~——9 (DEX-:0 of i+2$ih2 = 0 005x20 -> 1:11 111' 2— 2) s'hX2—é —-; 222E711}? 5 G (6) 4. If f(:1;) = ln(:c + 3) find a formula for the inverse function f “1(x). K3=§(><) 2:1) 7;: g"; , W to 42F" 9*" lino-1'3 (Azflmbufs) 48%: 7H-3 x x =.e‘"3 1 7‘ 10—106): 6 —3 E 94(3):.6413 -7 § (x)=e ’3 (4) 5. Solve each equation for :13. QP-C’fidx/L NFC \ b ”:5 __ —- w - W “M ML" -Ea $2-5” 'f 1 (6) 6. If f($) = 1:2—1 1 m7é explain Why f is discontinuous at a: 1. 1 if$=1 * gum 21-2. :L- m-» :11 L :2. @ 99:1{0'} 7(—)‘L x1... x3117t+1)(xv1) 7.27; 7+1 2— 30(1):;4 ‘ 3C (0 ob‘swvii'muom array]. becmASfl £qgé¢ «1) E] (6) 7. Find the exact numerical value of the following: QPL’ earl NFC (a) log 9641117 :3 Q“ 79-.- 2; MA 165 EXAM 1 Fall 2008 Name —___ Page 3/4 (10) 8. For each of the following, fill in the boxes below with a finite number or one of the symbols +00, ~00, or DNE (does not exist). It is not necessary to give reasons for your answers. 2V“ M NFC (a) lim COtIEZXUr‘n £9225, : -00 (b) lim .3: = 21m X z'flm .3“, ' 92—)0— Ismxl XMT""SN‘X 39’“? Sn»: —f1 . \/7_" _ . (d) aclirgiocosa; = DN E _ ,_‘_ D N l: (e) lim 2i‘C—‘O’LUm 2(X’SZ:2 $—)3+ $—3 ‘ 3‘63"- 1'3 (6) 9. Find the equations of the vertical and horizontal asympotes of the graph of y = 5932—2zv+1 _ ,2 m- £00 -.-. bx -2><:L 24‘ l (“190(4) m C :..m .'. _’ l ‘ x—a(—1)* ’0 "x- 4. v: v». @m*ng)-;OO 'x:2v>\/A 7w . Rm 3509:“ b”fem [maggfia nm ‘ ' P ‘2 . " —-1 Q X—D Yam-co ”’X . 3—9 “1'9";3 1 (8) 10. Show that there is a root of the equation 3:2 — x — 1 = in the interval (1,2). x + 1 State the name of the theorem you are using. x2_ ‘)( — 1 _. .1.” : O ‘ x +1., . {'09 : 7247C ’4, _._....fl:.———- © f {’7 OOMI'WM on L132} 1+1. w) 21-1-1~}£:v%<0 @ . iCz):4—2«1—%::.%>0 @ 9(1><0<g2.7_ EKG-46 PLov Some CE(4«-,2-} bk?) CL; Iniext'meclinL \fm Theorem @ MA 165 EXAM 1 Fall 2008 Name ____— Page 4/4 (10) 11. Find the derivative of the function g(t) = x/t using the definition of the derivative g’ (t) = gin?) MW. (0 credit for using a formula for the derivative). % gm : Um %Ct+k)—%(t) 2%,,” w @ 1’1"") 1') lap-90 h -_=. hm fill; 49: {at +5; 41°th Wham hag k .m—HE omfsmow OIL “3'0 two me' . 1 ' =t‘m W9: 4. (29 ' 2f? . E (8) 12. Find an equation of the tangent line to the curve 3/ = mfi that is parallel to the line y=1+3$ Tu saw, °t mum: 3=1+5>r (a a (23 v _. 3/1 ,cwcve. .xx (16) 13. Find the derivatives of the following functions. Do not simplify. 4151'» an}. (a) gft)=4sect+tant. NFC '4“! ~:: ' 4— s eclfwnt ';;CC2 i" (b) y = e‘”(1 + cot cc). .566 (C) f (00) = sinx' (d)u=€/i+4x/t_5. 5/ .—. '/ z _. ‘ V. ”t 5+“ (fir—ft % +101}??- m ...
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