{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

exam2sol - Math 16A(Winter 2009 Kouba Exam 2 KEY Please...

Info icon This preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 16A (Winter 2009) Kouba Exam 2 KEY 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 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 7 pages, including the cover page. 6. You will be graded on proper use of limit and derivative notation. 7. Include units on answers where units are appropriate. 8. 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 2 3m+x_2 +511 (2614—57 2‘ d.) f(m)=a:3-sinw~cosac WW WM] D 1 .1 . 3 3 - - *3? $é<2zéximxmx+ X. mx2wx+ X MX- WK 2.) (8 pts.) Solve f’(a:) = 0 for x, Where f(:1:) 2x4 — 8x2 . .9.» 41(6) : (49(3- léx 3) (8 pts.) Solve f’(a:) = 0 for 3:, Where 0 S m S 277, and f(x) = 2sinm —— \/§-x. Q» ~P‘Cx/z; RMX~W§ =0 -—> 7/? 004x31: ’a 4*; 7 Wu“ ch U17" T b/ 6 4.) (8 pts.) Sketch a graph of the derivative f’ using the given graph of f. 7 $— ZL' f(33 + A56) - f(x) 5.) (8 pts.) Use f’ (m)— — Aligo A3: to differentiate f(x) = x + 3 . _ x+Ax _, >< ¥\<><)~ M x+AX+3 “3 AX—> o M (W )Lx+32 - TCK+AX+3JX 4’” 0 LK+AX+ 3) LX+3J : M fiWfieflRM 2</%:‘);*% 4°90 CK+AX+3) 0% 3/ AK ‘ M 3' M ‘ Ax—ao CX+A><+ 3’) Q<+ 3] 79K ” 3 __ 3’ — Q<+3j (Ha) ’ Q<+3/ 7‘ 6.) (8 pts.) Find all points (9:, y) 011 the graph of f (m) = x2 — 3:5 with tangent lines to the graph of f perpendicular to the line a: + y = 2 . SLOPE 01W KW“? a th‘KJN‘ iv m:-( M 340105: of J—M X4 [Mflij #Cx :cixv3 a (RX—3:! -> RX:<1 A X152] jet-ml 7 ) (8 pts. ) Determine an equation of the line tangent to the graph of f (x) _ m2 —— 33: + 2 at a:- — —1. e—e-¥&2: cw< 3 ‘Ar’5L0p5‘%«tafij*“§L M20 m:~?612:2(~/2 3:-'/~ j~é: ‘5/CX+I) —-> j-é:—5’Xv5’——% yz—5X4—l 8.) (8 pts.) Find all points (:13, y) on the graph of f(:£) = 4x — x2 with tangent lines to the graph of f passing through the point (2, 5) . M, L.- Ad M 92~>< ~, 5,qu-va] 9~~ X : xl~4x+5' a~>< 9 IL] m:yl: q~2x J x’iqm—f: q_ ax—-> xiwm—f avx 9.) The given graph represents the amount of money M (in $) that you spent during the first week (7 days) of winter quarter. i y.. i i . , i , . .i .. . _ . , = ' . _ 2 , ‘ '. (5 pts.) Estimate your average spending 1' flaw—e, (0/0)) (3/3767 M ARC/3 375/0 1 ifilasi/W 3.. ate ($/day) for t = 0 to t = 3 days. 3~o your instantaneous spending rate ($ / day) when t = 5 days. b.) (5 pts.) Estimate —,__;_,Wc iii— z$ IKQ- ,. 3V3~ qg/Aogé c.) (3 pts. each) i.) Estimate the specific time t at which you are spending money most rapidly. ii.) Estimate the value of this rate. L. ] ‘E z a W 3 W .. 61 u») :xzc, : xx 2: ——;§ = Moo/do; ‘ EXTRA CREDIT PROBLEM— The following problem is worth 10 points. This problem is OPTIONAL. 1.) Determine the area of the semi—circle inscribed in the given isosceles triangle. ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern