Sol-165E1-F2002

Sol-165E1-F2002 - L MA 165 EXAM 1 Fall 2002 g Page 1/4 NAME...

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Unformatted text preview: L, MA 165 EXAM 1 Fall 2002 ' g Page 1/4 NAME, GRAome KEY STUDENT ID ‘ RECITATION INSTRUCTOR RECITA’I‘ION TIME DIRECTIONS 1. Write your name, student ID number, 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. . 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. No books, notes or calculators may be used on this exam. w (2) 1. Find an expression for the function whose graph is the top half of the circle (x—1)2+y2:1. NPC ‘(5 t m f(x)= V1 , (791)); Li] (4) 2. Find all values of a: in the interval {0, 2%] that satisfy the equation 2 cosx — 1 = 0. . D) 5 T7 w 3 -1 -11— -—1 (it ,lov mCL extva. animfi“ (8) 3. Let f (:v) 2: 2:1: + c and 9(31) : 3:1: + c2 where c is a constant. (a) Find the composite functions f o g and g o f. I g—o ): 9500 :2<§><)+C O a: 2 1. . ( ‘5)!” “Jews“ (f g)<) 6x +2c +c mg) . _ 'é- O m: , 2 3 (fiilwwflicxfiflflv’r: (g f)() Gx+c + c :th +6) + C WC (b) Find the value(s) of c for which ’ f o g : g o f. CDQ 9v 6x+2c2+ C 2: Gx +c7’+3c. cz—QCSD —) (130,2 la: 0) i - (10) 4. Write the equation of the graph that results by (10) (10) MA 165 EXAM 1 Fall 2002 " Page 2/4 ’ Name: (a) shifting the graph of y = e” 2 units downward (b) shifting the graph of y = e“ 2 units to the right (c) reflecting the graph of y 2 61 about the :L'vaxis (d) reflecting the graph of y 2 6* about the yeaxis * 1 (e) reflecting the graph of y : efi about the x—axisand then about the. y—axis . \a : ~— 8'“. . . _1 . . 1 +336 .7 . 5. Fllld a formula for the inverse f of the function f (2:) = 5 2 and give the domain —' 17 f ‘1. _ _. 4 Of%: 1+3): @ V‘9'&(’"¢:> Xzi co) - B—ZX 5'3 ¢2x%:1*3x 5% «i. a x (was) .. 53’1 ‘ -1 5‘ «t X”’-3+9.~3 “8 (% “£573 domain of f"1 : (—00, 43% U ”3/069 @ x ' 9; 4CD x¢—% ' 6. For each of the functions below find the value of k. such that the function is continuous in R, or state that there is “no such k”. 552—9 , . . (a)f(x)={”—‘x—3 “#3 Confirms» Pf an ”3 k ifz=3 (Jeni. at i=3? _ Linn 5:1? :Qim (X+5)Cx-3) :6 cont. ff {wré $2+5$+4 . (b)f(fl7)={ x—l 1M?“ confinmm [Lav “flit x219}, k H$21 00» 0: x=i? EJ'W x2+~°x+4 2+0“ 'gxotfid «PC x—rL‘r x‘j' ' m and, k MA 165“? EXAM ,1 ' _ Fa112002 Page 3/4, Name: (18) 7. For each of the following fill 111 the boxes below with a finite number, or one of the .3 symbols ()0, —00, or DNE (dOes not exist) It 18- not necessary to. give reasons for your answers _ 3,15: ‘Lofi Aztlan carveci'answen’ (NFC) (a)lim 67:00 t r 3265+ 27*5 2 0)) lim sin a: =¢th S '31th 1;: 2.61m “hi 2 t—JZX Y . ~ * 2) t , 1: ’ Lf‘l‘fi as 2i“ 1’, ! (e) mm 11129131.” 150} 4 x l 1.1—“. tum 4!- 3M ) 1 UN E qu’ le “X"?o (6) lim CSCIB= (Linn _.5;.———- 3—9.3 ”Ho” - X—ao" 51117 Show <0 {.01- x<o qu- dose to 0 , w 51'“? -—-’G 0.0 XaO — 1 . _. + 0 (9) 11m ———x— 00 ~ QM” KW $4100 :12 — ’10 X #’00 \G ’—» l O ‘ (f) lim ln(e$ ~1)= 11:4 0+ X (10) 8. Find the derivative of [(56) 2 —2 using the definition of the derivative: , :1: f,(37) : lim f($+ h) ” ft”) h 0 h (0 credit for using the formula for the derivative). ._..) . g/(x) :%:10 W ’Hhh' (7‘) ‘m UTE—PT)"- 33'. n \w-aO \n —— 'm X2 ”(whiz , 1W, x2424,” —1q l1 “*0 k (x-rh’f‘ x2 V190 \n (X 141)?” x2. : QM ~2x—F _~ —-2x __‘__2_’ MA 165 EXAM 1 Fall 2002 Page 4/4 Name: (10) 9. Find the values of the constants a and b so that the curve y = 0,372 +ba: passes through . the point (1, I) and the tangent line to the curve at (1, 1) is parallel to the line 3; : 33:. (’1’) In Ohm wu—e we» iza-kb @ firiax+bjwlwn x:=l 51:51:34,921, .313 g; Qqéaé @ p Cub: Pgsa (1:1; bz—j QUE—vb: NFC (a) y=$f 2521/; S 9/2,. x3»; "7 M 9— 0» ms) 2mm lgfx):£"g¢c2x +31%)! E} / X 2. N £00 ":8 $£Cx +8 tawny __ _. v '_ dime umsxoas . (C) 903) ~ 1:02:37 %’(x}- ('Hmzlziggyix)?~ x (5?” :_ (l+$l‘fl>‘)(*$5mt) -— w'sxcmx ’ ' ’ (*1 + anw)‘ 2. . _, —smx -—$mqk-m>w I+Sm7< :_ l _ I +S\‘n:x‘ W-Pfirnx) \+$n’\>( -1 PL (f «'m't'ad qésw 3/7)}? Larva} (mull ‘1 “\gjm (“cm “A S‘mM/l'alm’é (6) 11. Evaluate the following: N PC (a) sin(7re_h‘2) "3 Sf” (n- 2153.) :Slflf? 3%.:1 I . 1 a (b) 1321110711092) 2 him (W ‘2‘) n; all E] ...
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