exam3sol01

exam3sol01 - Math 16A (Fall 2011) Kouba. Exam 3 Please...

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Unformatted text preview: Math 16A (Fall 2011) Kouba. Exam 3 Please PRINT your name here : _______ __ Y 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. 3. No notes, books, or handouts 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. 5. Make sure that you have 6 pages, including the cover page. 6. You will be graded on proper use of derivative notation. 7. Include units on answers where units are appropriate. 8. You have until 2:00 p.111. sharp to finish the exam. 9. The following trigonometry identities are at your disposal : (1..) ‘sin 26 = 2 sin 6 cos 6 b.) c0520 2 2cos2 (9 ~1 = 1 — 2 sin‘2 0 ’1 - ’) = cos” (9 * sm‘ 6 1.) (6 pts. each) Differentiate each of the following functions. DO NOT SIMPLIFY ANSWERS. a.) y : (3.102 — 2.7;)‘1 ~l. 59-» 7‘: «5&3 m- (Md) b)y=rc-\/2+:c3 ._//.z- .2. 2., y’: x BECHXS’) '3x + (I) R+><3 . 3 ' C.) y=sin3(sec(2;1:)) (queV‘S I (. M) M) 1x) 9a, y‘: smilméwl- Mémcax} 2.) pts. each) A ball is thrown straight up at 48 ft./sec. from the top of it build- ing which is 160 ft. high. It's height b, above the ground after t seconds is given by so) = —16t2 + 48t+160 . Q ’ ‘ a.) How high does the ban g0 ? kw W ‘, 4... 5 : 5 48,3M. S‘C-H': "3.2++ 4? -.-. o .7 75; ,, M 584% 5(3. z-(W b.) How long is the ball 11:23 an. 17 : at)“, (2‘ 5:0 -7 35L"; Mfwz 3(1:):~let"+qy++ (co 2. watt”: 3-e-to)=-recb~5jee+;¢ : o a f=5m. C.) What is the balls velocity as it strikes the ground 7 M 5'“) = “301(5) + H? 2-411 #-/m. 2 3.) (10 pts.) The base :1: of the given right triangle is increasing at the rate of 4 in. / see. How fast is the hypotenuse y of the triangle changing when the base is .7; = 12 inches? :1.) Assume that y is a function of :1: and 6.B + 5/2 = mg + 4' . a.) (5 pts.) Determine the slope of the graph at the point (0. ‘2). 2+ 6+ 277‘ s xY‘+ (1H —J~ mnyy‘: 1—9 a YICQsY—X): vavy) Mug-— Kwflvaz w SLOPE 7!: 23,: @ M@ .. h.) (5 pts.) Determine the concavity of the graph at the point (0,2). 2% Y”: (RY-«fife Oval-(3.7L!) X30 ng (EV—le I Yl~-/ u~ (VHF;- - .. Ac ‘( v W: T‘:;@ M @ c.) (3 pts.) Draw a rough sketch of the graph near the point (0, 2). 5.) (15 pts.) For the following function f determine all absolute and relative liiaxinium and minimum values, inflection points, and x- and y-intercepts. State clearly the x-values for which f is increasing (T),_decreasing (i), concave up and concave down Neatly Sketch the graph of f. f(rc)=;L'——6\/E '. 6"“ K10 D l -1 J. -414 No 2' : 508/1 //////" 4' + 4’ £“ _‘_—__——-——-——- X30 x-aoo _ M wribfi~éj x-w . . . . ch 6.) (l) pfs.) Assume that y is a, function of 1‘. Determine y’ = —J (LE I D m — m8 = — mm .4. 363x01)”. (3-1!): mum‘fiaj- JLYY’ ——> 14(3x~~()7~ as’Lsxwfil : ax~ :LY-‘I‘MJ‘CY‘7’9 a‘l‘l‘A—e—c" CY‘V- 8C3X~Yjwvl : ax v 5234 (3x-yj7_-, Y" [QYA’f-‘L‘f‘j—fiéwvflq : ax-“ L3x-yj7—9 '7 7!- axv M (3x42 aymfifib 3’ Clix—“()7 7.) (11 pts.) The radius 'r of a right Circular cone is increasing at 4 cm. / sec. and the height IL is decreasing at 5 (TIL/SEC. At what rate is the volume of the cone Changing when 7' = 3 cm. and h, : 2 cm. 2’ Assume that the volume of a right circular cone is V : (1/3)7r7‘2h. 3:: ': (2(sz - Max) : ngx~ijcwflX+ MK]: 6 —-9 MK~szo q mxth—a x: 1;: ——=7 mx+~€nxzo- mx:~/almx -> K:3TT- x:o x217! ngf 3:77 fl. 21:31 Y: ’4‘ M _ EXTRA CREDIT PROBLEM— The following problem is worth 10 points. This problem is OPTIONAL. 1.) Find a function f (:13) Whose derivative is .p'oq/ :_ 3K‘M1Lx3)-[3x3cov(x3) + M 00)] : : qXVM‘Lx3)mé<3)-I- 3x93414903) : x3. smaaflmcxv-sxl + M3“ 3] D M3Cx3) 9"" CPQoDuC‘r Race] .2 D m3éx3)} A0 41R): K3M3C><3j 6 ...
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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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exam3sol01 - Math 16A (Fall 2011) Kouba. Exam 3 Please...

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