pracexam2sol 17A - Math 17A (Fall 2006) Kouba Exam 2 K E \/...

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Unformatted text preview: Math 17A (Fall 2006) Kouba Exam 2 K E \/ 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 NOT receive full 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. 5 6 7. Put units on answers where units are appropriate. 8. Using only a calculator to determine limits will receive little or no credit. 9 . You will be graded on proper use of limit and derivative notation. 10. You have until 8:50 am. sharp to finish the exam. 1.) (7 pts. each) Differentiate each of the following functions. DO NOT SIMPLIFY ANSWERS. a.) y = 123/4 + \/123 —- 2:13"7 I) l 3,. 8’ t 44+— 0 -—J\-~7>< ~————> 4/00: (3*X)1 ~1 Q 4/2 1 L JPM): 3364 +Q><1+fl - fizfixflvq - 2x 2.) (5 pts. each) Let f(x) = m(5 —— ac)4. a.) Solve f’(x)=0for;v. L #(x): x. qu’vxflfi—lfi— a)(5_><)" : (E-x)3.[-—<I><+ (s—xn : (s—x)? [525x] :0 a x26; x: l b.) Solve f”(:c)=0f0r$. £“L><) : (5-x)3E5] + 3(5—x]°2(-I) [321ij = ~(5—xfi-[5C5—x) + SOT—fig] :. ~(5—x)1[25’«5X+15’-!5’X] : ~ Ls—><)l[<{o~.zox] :o ~+ X253 X: 5{ l9 3.) (9 pts.) Use the Intermediate Value Theorem to prove that the equation x3 = 4 — x is solvable. This is a writing exercise. You will be scored on proper style and mathematical correctness. x3:4«x——a X3+X~flzo AoM-W ,wVQ m:o , W MX~NM W‘FMQMWM’Q. M ¢(|):~;)Je(1):@) W9 m:o osmomii tcz]. Mm W III/a]. fmlrw‘r MM airs] tscsg/ M +LC):VV\J L67 03+C~<{:o 4.) (8 pts.) The following table of values uses the Bisection Method to estimate the solution to the equation f = 0. Fill in the missing 10 numbers in the table. a b (1/2)<a+b) f(a) f(b) f((1/2>(a+b)) “Kl-m -_ m - 3 5.) (9 pts.) Assume that y is a function of m and my2 + y = x + 3. Determine an equation of the line perpendicular to this graph at a: = 0. ALKXZOJM (ong—FY: 0+3 ———> Y: 3 ><Y';‘wL Y: X+3 2* x-aYY'+cl)7’~+ Y’: 1+0 a Y (aw/+1): #719 VI: 1-7" 9 RXY+7 X:C>/\(:3-——> \(i: 1’? 2“?W~l—W .c. 7.) The given graph represents the mass M (grams) of a benign tumor from t = 0 months to t = 10 months. i.) t = 0 to t = 3 months. ISO—n15 ( 4 I c I 956 a.) (3 pts. each) Estimate the tumor’s average growth rate (grams/ month) for ID 781 ii.) t = 4 to t = 7 months. MC?) v MG!) MC" ’7 — q 3 25:2 3 [5’0 ~ .200 4/ w 3 2: #67 M- M. b.) (3 pts. each) Estimate the instantaneous growth rate of the tumor when i.) t = 1 month. IQQ: MICVX Wow/5' 5—0 : W. W. ( I l \ ( ii.) t = 4 months. IRC = Mkflz o m W. c.) (4 pts.) Estimate the specific time t at which the tumor is growing most rapidly, and estimate the value of this rate. +223”, Mn IKQ:M'(3/x .275 2.3 N N [(7.5 7C1?”- xw~——o - 8.) (9 pts.) Consider the given right triangle with edges 1‘ and y. If length at is increasing at the rate of 2 ft. /sec. and length y is decreasing at the rate of 5 ft. / sec., determine the rate at which the perimeter of the triangle is changing when :r = 3 feet and y =2 4 feet. 2 our '1 M‘ 1 AP :3 _ I»? xhvlzz—lr-a Z:\/X'l+‘l’~ Y 3;; 254: we 2 -I : (2+ (-5]+ 3‘: but] '2. gaé3jé&)+ £10066“) : ~3+$§1a—qo} : ’3~—2-5’ = *‘SX/{X/M. 9.) (9 pts.) Find all points (32,31) on the graph of f(x) = x2 with tangent lines to the graph of f passing through the point (0, —1) . SLOPE «(M L Ac : 52X 1 we) X~o _, ‘(H __ X244 ‘ x ‘ x / __..» X1: 1 ———=7 Xzil —> The following EXTRA CREDIT PROBLEM is worth 10 points. This problem is OP— TIONAL. - 2 - 2 - 2 . . . . Slnzc - sm sum 1.) Evaluate the followmg limit : 11m ( ) z—m cos2 x2 — 1 M MX'Z- MQ-fimxfl-Méaa‘mxi) .a X 0 : “fig. “(M/’1”) . M(M><"/ X—vo M2 Mxl __ (—4). (1). Mcmo) ~l Mo ~4 Lo) (I (t O (I ...
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This note was uploaded on 11/26/2010 for the course MAT 017A 69453 taught by Professor Craigbenham during the Winter '10 term at UC Davis.

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pracexam2sol 17A - Math 17A (Fall 2006) Kouba Exam 2 K E \/...

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