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Unformatted text preview: Math 21A
Kouba
Exam 3 Please PRINT your name here : __________________________________________________________ _ Your Exam ID Number __________ H 1. PLEASE DO NOT TURN THIS PAGE UNTIL TOLD TO DO 80.. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY,
ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. 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. 2. No notes; books, or classmates may be used as resources for this exam. YOU MAY
USE A CALCULATOR ON THIS EXAM. 3. 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. .4. Make sure that you have 6 pages, including the cover page. 5. On optimization (maximum/minimum) problems use a sign chart to verify the
minimum or maximum and list optimal values for ALL variables used in the problem. 6. You will be graded on proper use of limit and derivative notation.
7. Put units on answers where units are appropriate. 8. You have until 9:50 am. sharp to ﬁnish the exam. 1.) (7 pts. each) Determine y’ : :ii—y . DO NOT SIMPLIFY ANSWERS.
:1: a.) y : ln(sin :13) + log(cosa:) b.) y : (tan 51:)” 2.) (10 pts.) An initial deposit of $5000 in an account grows to $50,000 in t years. If the annual interest rate is 8% and interest is compounded weekly (52 weeks per year), what is
t ? 3.) (11 pts.) Find the point on the graph of y : nearest the point (4,0) . 4.) (11 pts.) Assume that y is a function of x . Determine the slope and concavity of
the graph of 13y : y2 — 1 at a: : 0,1; 2 1 . Sketch the graph near 13 : 0,y : 1. 5.) (10 pts.) Use Newton’s Method to estimate the value of (20)”4 to three decimal
places. HINT : Apply Newton’s Method to the equation :34 — 20 : 0 . Let :171 : 2 . 6.) (11 pts.) A cylindrical can with no top is to have a volume of 877 in.3 What radius 7‘
and height h will result in a can of minimum surface area ? RECALL : The volume of a
cylinder is V : 7r7'2h . I 7.) (11 pts.) Determine the height y and the base a: of the isosceles triangle (2 edges
are equal) of largest area which can be inscribed in a circle of radius 4 inches. 8.) (10 pts.) The edge cc of a cube is measured with an absolute percentage error of
at most 5% . Use differentials to estimate the maximum absolute percentage error in
computing the cube’s surface area. 9.) (12 pts.) A tank in the shape of a cone (vertex down) of height 5 ft. and radius 5 ft. is
full of water. If water is removed from the tank at the rate of 871' ft.3/min., at What rate is the circular surface area of the water changing when the radius of the water is 7“ : 4 ft.
? RECALL : The volume of a cone is V = (1/3)7rr2h. w SID E
VIE W The following EXTRA CREDIT PROBLEM is worth 10 points. It is OPTIONAL.
1.) Use differentials to Show that v4 + h2 m 2 + (1/4)h2 for small h. ...
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 Fall '07
 Osserman

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