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exam1sol01 - Math 16A(Fall 2011 Kouba Exam 1 KHZ Please...

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Unformatted text preview: Math 16A (Fall 2011) Kouba Exam 1 KHZ ____________________________ __ 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 STUDENT’S 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. 3. 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 NO 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. Make sure that you have 7 pages, including the cover page. You may NOT use L’Hopital’s Rule on this exam. You may NOT use shortcuts for finding limits to infinity. 0039‘?” . 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 sharp to finish the exam. 11. The following trigonometry identities are at your disposal : a.) sin 20 = 25in0cos€ b.) c0329 = 2cos26 — 1 =1—- 2sin2 9 = cos2 6 —— sin2 6 1.) (9 pts. each) Determine the following limits. 22-1“:E,” . \4’(_‘ & . 5 6x3+6x2—5m X9” '_ M ’X d.) ——————————-32 2” 7 .-—-/ ._ “H J/ Xfiw gflglfltl Xk >< ><9\ — Q9+G~O : 00 3~o+o 2.) Consider the function = 2 + 4cosx. a.) (4 pts.) Determine the domain of f. b.) (4 pts.) Determine the range of f. -( S W X S 4-] fl "‘{ééhum><i q—e -&:3;+qafifl<éé)‘4o KW: ~02:\/§<o {I} 3.) Consider the function f :2 4 . — :r a.) (4 pts.) Prove algebraically that f is one-to—one. 58% cm : lint) «Ix. «ya: «we, W X q’X/ q-XA _ 4 F;a‘fi..KA 4% *7 Xl<,%_xfl\):x)\<f’("xl) #44 I—‘l b.) (4 pts.) Find the inverse function, f“1. xcw/jzv—e qXVXYIY ~—> «(xzwi a 4x: Y (my ——a _ 44x ~t ~ qx Y” ><+r "3” *CX)‘ 'YLT 4.) (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 :13. Start by drawing A+Bm, ifx<—1 \( a “fake” graph: f(x) ={ 3 , if -1 3:3 <1 332+B, ifle 5.) (8 pts.) Solve the following trigonometry equation for 0 , 0 S 6 _<_ 27r : sin 20+sin6 = 0 (HINT: Use a trig identity from the cover page.) QMGWQ+M®:O ——7 6.) (8 pts.) Use limits to find the equation(s) for all horizontal asymptote(s) for y :: [3:4 . YOU NEED NOT GRAPH THE FUNCTION. M 3>< .3 M .__§_>_<__._, _ M 3>< x—J‘oo \lXMq xii” VX’Z Mia/JV) X93100 1&1 H- £1 94% 36' p 0 ~ M 3x ‘ X900 X Hafi— ’ 4M 3 .. \lH—O ’ W X>o _, 3 ) w x>6 1:0 3 44'” X<O ~3 J M X<O 7.) (8 pts.) T he 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 Am a (we) ——? (00:4X'L—-=7 XL:&5'~9 X: 5/ M M: W: “41* CH 8.) (8 pts.) Determine the center and radius of the following circle : m2 — 6m + y2 = 16 x*~6><+¥*:(é a (xi—ex+9)+ Y1: “0+7 ———7 CX*3)&+(Y—o)l’: .5’7‘___., W : (3/0) W: b“ 9.) Determine the following limits. \l I I . x 3 a.) (3 pts.) $133+ 3_$ : F P: N w 3.! X3 3 ' l b.) (3 pts.) lim $+1 : M X+ I ——’/ X5! Y£( The following EXTRA CREDIT PROBLEM is worth 10 points. This problem is OP- TIONAL. 1.) The function, = $6 — 21:3 for :L' g l , is one-tO—one. Find its inverse function, f‘l. szt~a><3a sowiww x: Y‘ta‘rg/‘z (WW 7]” K44: \(b’DZYBwl—i é KM Cé'gjav XC/y‘ti “A? x+(: (Y3~%)2'—% /‘ WW§71= (Yi+)*'—% W : ($34] ~> (YilflaYZISO) —Wfi:~0%ffi ~ ><+l ‘ 734% \(3: (—~ ><+z —% ...
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