03faex2 - ‘4 MATHEMATICS 112 EXAM II Name RE“...

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Unformatted text preview: ‘4. MATHEMATICS 112 EXAM II November 11, 2003 Name: RE“ Instructor and section: m 1. 5. 6. 7. 8. There are 10 problems on 12 pages (counting this page) + 2 pages for scratch work. . No graphing or programmable calculators are allowed. Scientific calculators are allowed but are not needed. . Give exact answers (fractions, square roots, etc.). Decimal approximations will not receive full credit. . Do not simplify your answers unless specifically told to. Answers such as 2V25 6 3T+ are perfectly okay. Answers such as 3:1: + 4 = 7a: — 2 require more simplification. x: No notes or books are allowed. Use only the scratch paper provided. Show your work and make your methods clear. Unjustified answers will receive no credit. Put your final answer in the box. 273—7 1. Let g(t) = Simplify the following as much as possible. (a) (5 points) Find g_1(t) Answer: (b) (2 points) What are the domain and range of g(t)? Answer: (c) (2 points) Evaluate (g o g‘1)(l5l)? Answer: l (53: + 9)(2z — 7) (ac — 2)(:1: + 1) h and vertical asymptotes if any. 2. (9 points) Graph y = Label all z- and y-intercepts and horizontal 4 3. (10 points) J .W. runs a ranch and has $6000 to spend on fencing. He wants to put a series of 15 corrals as shown in the picture. However, due to strong winds out of the west, the North-South Fencing costs $10 per linear foot while the East-West fencing only costs $5 per linear foot. Find the dimensions so that the total enclosed area is as large as possible. North ‘ Answer: ’ 4. (a) (5 points) Graph m(z) = 2(5a:+ 20)2(14x - 7)3. Label all m- and y— intercepts and horizontal and vertical asymptotes if any. (h) (3 points) Find the values of c such that the minimum value of h($) = $2 + cm + 7r is —1. Answer: (0) (2 points) Does g(z) = (x - 2)4 + 17 have an inverse? Explain how you know this and give an example to justify your conclusion. Answer: 6 5. (9 points) Captain Jack and his band of jolly pirates are stranded in a rowboat. They are rowing due west straight for Treasure Cove at 5 leagues / hour. When they are 75 leagues from Treasure Cove they spot the infamous ship Black Pearl 100 leagues directly behind them (due east) and closing! The Black Pearl is also sailing due west but at the much faster rate of 15 leagues / hour. Will Captain Jack make it to the safety of Treasure Cove before they are overtaken? If so, how far behind them will the Black Pearl be? If not, how far from Treasure Cove will they be when they are caught? (Note that a League is a unit of distance) Will Captian Jack get Caught?: Distance: 6. (a) (6 points) Graph y = 2 + 10g10 (:c — 3). Label all a:— and y intercepts and horizon- tal and vertical asymptotes if any. ' l (b) (6 points) Graph y = 6”” — 2. Label all x— and y— intercepts and horizontal and vertical asymptotes if any. 7. (10 points) Find the average rate of change of f = —-$2 + 7:1: — 3 on the interval [5 — h, 5] where h > 0. Answer: 8. (6 points) Graph f (x) = —-\/—:c + 2 —- 3. Label all m- and y— intercepts and horizontal and vertical asymptotes if any. 10 9. (10 points) Let f(.7:) = as much as possible. 13$ — 4 3 . . . 2x + 1 and g(z) — x _ 1. Fmd Slmpllfy your answer ' I 10. (3 problems, 5 points each) Simplify as much as possible the following: Answer: liq: 3 1—1: " z—2 (b) x2 + 2x — 5 l Answer: . Third problem on other side of sheet. 11 (c) W+ 2525422 - 25x2y222 12 Y SCRATCH WORK 13 SCRATCH WORK 14 ...
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This note was uploaded on 08/08/2008 for the course MATH 112 taught by Professor Carlson during the Spring '08 term at University of Wisconsin.

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03faex2 - ‘4 MATHEMATICS 112 EXAM II Name RE“...

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