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Unformatted text preview: Math 168
Kouba
Final Exam Print your name here. Your exam ID # 1. PLEASE DO NOT TURN THIS PAGE UNTIL TOLD TO DO SO. 2. No notes, books, or classmates may be used as resources for this exam.
You may use a calculator. 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. 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. The best way to get maximum partial credit is to
write neatly and be organized. 4. Make sure that you have nine (9) pages, including the cover page. 5. Include units on answers where units are appropriate. 6. YOU WILL BE GRADED ON PROPER USE OF integral (l), dx, du, and dv
notation. 7. There are 5280 feet in one mile. page 2 of 9
1.) (10 pts. each) Integrate. a.) S_eL__ ax
50+e7X b.) IxVSx dx 0.) Jxln(x+1) dx d.) J(cosx + secx)2 dx page 3 of 9
e.) I tan3x dx f.) I(Inx)2 dx x+3e' 9051+ X dx 2.) (10 pts.) SET UP BUT DO NOT EVALUATE the integral(s) which represent the area of the 2 regionboundedbythegraphsof y=3x3x21Ox and y=x +2x. page 4 of 9
3.) (8 pts.) If you deposit $1000 into a savings account earning 5.75% annual interest compounded monthly, how many years will it take for the amount to grow to $4000 ? 4‘9 4.) (8pts.) Findyl=dy/dxforexy=y3+x2+lny.
5.) (8 pts. each) Consider the region bounded by the graphs of y = \1 2 x and y = (1/2) x.
SET UP BUT DO NOT EVALUATE the integral(s) which represent the volume of the solids formed
by revolving this region
a.) about the xaxis. b.) about the yaxis. page 5 of 9
6.) (8 pts.) Compute T4 , the Trapezoidal Rule with n = 4, to estimate the value of the following definite integral. Write your answer to three decimal places.
1 jlog10(3+2x) dx
1 7.) The number N of wild hogs in a game preserve after t years is given by
400 1+2t fortZO. N: 500'. a.) (3 pts.) What is the initial number of wild hogs ? How many wild hogs are there after
t: 2 years ? What does N approach as t approaches infinity ? b.) (5 pts.) At what rate is the number of wild hogs changing when t = 2 years ? c.) (6 pts.) What is the average number of wild hogs in the game preserve from t = 0 years
to t = 2 years ? 1 page 6 of 9
8.) Let f (x) = 415? for 1 S x S 9 be a probability density function with continuous random variable x representing the number of hours per week that Davis commuters spend driving
their automobiles to and from work. a.) (5 pts.) Verify that f is a probability density function. b.) (5 pts.) Compute the mean u = E(x) for x. c.) (5 pts.) Compute the median m for x. d.) (5 pts.) Compute the variance V(x) for x. e.) (2 pts.) Compute the standard deviation V' for x. f.) (4 pts.) Compute the probability that x is greater than or equal to 6. page 7 of 9
9.) (10 pts.) You are going to play a lottery game which allows you to randomly select a ticket
from a fish bowl containing 300 tickets. Thirty (30) tickets are $25 winners, five (5)
tickets are $50 winners, and one (1) ticket is a $200 winner. If you must pay $5 for the
opportunity to select exactly one ticket, what is your expected net gain ($) ? 10.) (10 pts.) Find all critical points (x, y) for the following function and classify them as
relative or absolute maximum or minimum points. f(x)=lnlx  ln(x2+4). page 8 of 9
11.) (10 pts.) Assume that while chewing on Double Bubble bubble gum the amount of sugar in the gum decreases exponentially. If, after 1 minute of chewing, 75% of the original amount
of sugar remains, what percent of the original amount of sugar will remain after 10 minutes ? 12.) (10 pts.) A large hailstone falls from a cloud at 15,000 feet elevation with initial
velocity zero. What is the hailstone's velocity in miles per hour when it passes an airplane flying at 11,864 feet elevation ? Assume that the acceleration due to gravity is 32 ft./sec.2 page 9 of 9
EXTRA CREDIT The following problems are optional. Consider the given symmetrical
4sided pyramid of height 3 ft. and with square base of area 16 ft. 2 a.) (5 points) Compute the total surface area
of the pyramid. b.) (10 pts.) Find the radius of the largest sphere which can be inscribed inside the pyramid. ...
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 Spring '10
 Kouba
 Calculus

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