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Exam1sol11 - l\Iath 16A(Fall 2011 Kouba Exam 1 Please PRINT your name here<€ Your Exam ID Number 1 PLEASE DO NOT TURN THIS PAGE UNTIL TOLD TO

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Unformatted text preview: l\Iath 16A (Fall 2011) Kouba Exam 1 Please PRINT your name here : _________________ _-_<€._ ____________________________ __ Your Exam ID Number __________ __ 1. PLEASE DO NOT TURN THIS PAGE UNTIL TOLD TO DO SO. 2. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO COPY ANSWERS FROM ANOTHER STUDENTS EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO HAVE ANOTHER STUDENT TAKE YOUR EXAM FOR YOU. PLEASE KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK YOU FOR YOUR COOPERATION. $5. No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM. 4. Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting'work will receive LITTLE or N 0 credit. What you write down and how you write it are the most important means of your getting a good score on this exam. Neatness and organization are also important. 5. Make sure that you have 7 pages, including the cover page. 6. You may NOT use L'Hopital’s Rule on this exam. 7. You may NOT use shortcuts for finding limits to infinity. 8. Using only a calculator to determine limits will receive little or no credit. 9. You will be graded on proper use of limit notation. 10. You have until‘11250 a.m.l sharp to finish the exam. 11. The following trigonometry identities are at your disposal : a.) sin 26 = 25i116€050 b.) c0526 2 200526 —1 = 1 — 25in2 0 2 cos2 9 — sin2 0 1.) (9 pts. each) Determine the following limits. a.)lim .. x—>1.’L‘2+12—2 3 Hall b.) lim “3—4 {£431 fl” Rm ' x—m w :W+2 Z ’Y “2—H lim 9; 3~X ——l——‘ “3 X93 3X X‘3 . ~‘I : M fl ’— X‘fi 3X W) 7 l “00” 5" lim 6:3:651? #39” (OX-:ffl—E]? x—wo .1: —- a: " ~ “4— X" Km” 3 X xk oo+é~o : 00 3 x o 4— 0 no I! 8 $2—1 M (2<~/I)C><+I) _ L 2.) Consider the function f(;r) = 5 + 2sinx. a.) (4 pts.) Determine the domain of f. OW: avg/Q K~~M b.) (4 pts.) Determine the range of f. '“(éA/VVLXIS‘FI ‘—" “02$ gmxg ; ‘3 3 E 5+5ZM><£ 7 40’ flow/1%)“ I 35 Y3 '7 3.) Consider the function = I 3—1" a.) (4 pts.) Prove algebraically that f is one-to-one. iCXJziéxa/ 3X1” a6: 3&1— Ml % X; 2 X1 '—> 3X, :1 3~Xl ___7. X .. 1* X01, 4’0 ‘P/Q. l‘i. *5 XIC3”K.L)=X,LC3‘XJ b.) (4 pts.) Find the inverse function, f‘l. :X 3X~><Y:Y a “kw/“(4’ 3X:\{C><+l)-'? Y: 3” *‘e X+f ~I h 3x “D W“ ><+z (10 pts.) Use limits and the concept of continuity to determine the value of constants A and B so that the following function is continuous for all values of :1). St Am—f-B, ifzr<0 a “fake” graph: f(x) = { 2 , ifO S (c S 1 2 x—A if$>1 Refilnefig/ fituda' ’ M (AM—IQ): 2% % art by drawing X~> 0'~ M (Xi—A) 1 Z X“, l‘l’ W1 wow» 5.) (8 pts.) Solve the following trigonometry equation for 0 , 0 S 9 g 27r : si1126+2 sin 0 = 0 (HINT: Use a trig identity from the cover page.) amg9+gpme:o_a amaeume+anmo:0~e awe Cwél—U =0 a ,M6:0 OIQ C0491~l 4, t 6:01TF/0’LT1’ 92W 6.) (8 pts.) Use limits to find the equation(s) for all horizontal asymptote(s) for y = . YOU NEED NOT GRAPH THE FUNCTION. . ' 3X . 3X M 7; M, :3 M ---—----——'-' X300 m x49» \lxl hie—:21) x—eiw 4351‘} 1+ gig,» ' 3)( M 3x M ) +3” x> o ’5 8 >< Ell X [-Q 2’ 3 .9 H-O ) {Mm X>o W 3 ) 493/7 x>o '" _ \ ~ 0 (:0 J 4.4/7 X<O 3 J M x< 7.) (8 pts.) The length of a rectangle is four times its width. Find the length and width ' of the. rectangle if the rectangle has area 100 square feet. 4X x (oo:><<‘{><) ——> {ooquL—a x": a5.» x; W: “41* 5 Ac) 8.) (8 pts.) Determine the center and radius of the following circle : r2 — 61: + y2 = 16 X°Z~6><+ W: (6 —-> 08- ex 4—?) + Y; 21M? —>7 Cx~ 3)J‘+ (Y—o)l*: 5 9‘ —-——-v W : (3/ 0 W : by .0.) Determine the following limits. a.) (3 pts.) Ill—+1; :1 -—-g-:; : + 00 2.7 ___>;_?+___ X13 ' ><+( l b.) pts.) llm IE+1 : W ’2 x—>0+ .L‘2—JI o-l " ~l ” \ w fl—eee—t = 7+ ~ ~ X30 The following EXTRA CREDIT PROBLEM is worth 10 points. This problem is OP- TIONAL. 1.) Evaluate the following limit : ‘lim ( V13 + 21' — \/.L‘2 + 2 ) “GO-00!" “30 : M szi—ax-lxvhzl (X'MX +V><3+9xl >900 Q X +5<><+V><1+<1) : M +01X~ /(+9\ x—vw an xh—a M ax~ .2 2. 1 K9 [786+ §)+\l)ika+~>a) C I ' a\>(.C1—~-_ JERle :x 1 if” W 4—7 l M We) l ,— Ozx Cl— /X) \ 92 xaw NHL-:2— K‘Wk l M /><) " )(—7 00 3: 21‘ XL H—X 4/ (4. KJ Z (l 150) : 3’2: 2 i _ ...
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This note was uploaded on 02/17/2012 for the course MATH 16A taught by Professor Sabalka during the Fall '08 term at UC Davis.

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Exam1sol11 - l\Iath 16A(Fall 2011 Kouba Exam 1 Please PRINT your name here<€ Your Exam ID Number 1 PLEASE DO NOT TURN THIS PAGE UNTIL TOLD TO

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