exam2sol 17A - Math 17A (Fall 2010) Kouba Exam 2 \( Please...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

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

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

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

View Full DocumentRight Arrow Icon
Background image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 17A (Fall 2010) Kouba Exam 2 \( Please PRINT your name here : ......... “Kg ______________________________________ __ 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. 5. Make sure that you have 7 pages, including the cover page. 6. Put units on answers where units are appropriate. 7. You will be graded on proper use of limit and derivative notation. 8. You have until 11:50 am. sharp to finish the exam. 1.) (7 pts. each) Differentiate each of the following functions. DO NOT SIMPLIFY ANSWERS. a-) y = 58—5/2 - (1/2)3B — \fi 4 3) ‘--5’ “7a ( 1 41 3/ * IX ’ a“ 3X boflm=i;? & D 1 ~ Unix) (ax— 5)~Lx——bx)0) "a +00” LL(+><)‘9‘ 2.) (5 pts. each) Let f(:1:) = ($2 — 4)4. 21.) Solve f’(:1:)= 0 for m. —D—-. 4‘JCK):LICXA~‘{)3~ C. O —-—9 w m = cxvmwwo A b.) Solvef”(m)=0fora:. —a¥@fi8X®£fl3A 3 L ~F”Q<) : 3x. 3L><£<zj 2x +3?) (28:4) 01 " XCXD‘V‘QQ‘L’GXA4— x54]: QCXE‘Q [vxalqjub e-mm “2 3.) (8 pts.) Use the Intermediate Value Theorem to prove that the equation fl = 3 — a: is solvable. This is a writing exercise. You will be scored on proper style and mathematical correctness. 6?:3—x—n ><-3’+W><_:o MM W\”~‘~O MHDx 4.) (8 pts.) The following table of values uses the Bisection Method to estimate the solution to the equation f(a:) = 0. Fill in the missing 10 numbers in the table. 5.) (9 pts.) Assume that y is a function of a: and 3:3 +313 = my + 8. Determine an equation of the line tangent to this graph at the point :1: = 0. X3+73=xy+37~¥D=2 3X’14—3y‘1y': X7’4.(12\/+o-4» 3V3J'~><7' = 7- WK ey'é’s’y‘ix} 172326 _, 9x \ a yl: 73X . A/{koang 7,) The given graph represents the weight W (lbs.) of a growing (freezing) and shrinking (melting) block of ice from t = t = 5 hours. ARC, I w(5}-wC2) £2. 8’ — 4.6’ » N “0.597 7‘ 3 5’“ a v W'//4W. b.) (4 pts.) Estimate the block’s instantaneous rate of weight change (lsz/hr.)vwhen t = 3 hours. c.) (4 pts.) Estimate the specific time t at which the block is melting most rapidly, and estimate the value of this rate. Mi “fix‘IE/lvw. 544 8.) (8 pts.) The area of the given semi-circle of radius r is decreasing at the rate of 67r in.2/min. when r = 3 inches. At What rate is the perimeter (including diameter of semi-circle) of the semi-circle changing when 7‘ = 3 ? 5L M : : 2‘: H w ) w:-—~Q7T‘/vv\./mwfl H M A A M“ d oi ~\__ V‘___,,— 1 .___C Lfi‘3F/WW Elf MAM—i 0w”. ‘_ ~ D i.\ 03‘ (RM wJ AM‘TMlL we 9.) (8 pts.) Find all points (any) on the graph of f z: 1:3 —— 3:62 with tangent lines parallel to the graph of the line y = 99: + 5. yqu+5L y’:q M SLOPE /‘ :BXX—GX : C7 h—>0 h I 3 WW My: swamp/w {fl-*0 M v l/l-ao The following EXTRA CREDIT PROBLEM is worth 10 points. This problem is OP- TIONAL. 1.) The m-axis is tangent simultaneously to the parabolas y = x2 and y = —(;1: —— 2)2 . Find another line which is simultaneously tangent to both parabolas. ...
View Full Document

Page1 / 8

exam2sol 17A - Math 17A (Fall 2010) Kouba Exam 2 \( Please...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online