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3 Pages

### final takehome(1)-1

Course: MATH 160, Spring 2012
School: Boise State
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Word Count: 545

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______________________ Final Name: Exam Take home portion. Please show all work. This is a calculus test, so I need to see calculus work. If you use a calculator to evaluate an integral, you need to show it set up. 1. Non-buoyant bulls and cows need to be pastured separately on a field bounded by a river. (The cattle don't swim, so there doesn't need to be any fence on the river side.) The rancher has 5000 yards...

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______________________ Final Name: Exam Take home portion. Please show all work. This is a calculus test, so I need to see calculus work. If you use a calculator to evaluate an integral, you need to show it set up. 1. Non-buoyant bulls and cows need to be pastured separately on a field bounded by a river. (The cattle don't swim, so there doesn't need to be any fence on the river side.) The rancher has 5000 yards of fencing. What dimensions will maximize the pasturage available for the animals? no bull bull river 2. On stage, a light is being lowered at a rate of half a foot per second, 5 feet away from a 6 foot tall actor. How fast is that actor's shadow growing when the light is 10 feet off the ground? light shadow (Hint: Use similar triangles to set this up. The Pythagorean Theorem isn't going to be very helpful. Also, it will be easiest to work with if you separate the variablesput the separate variables on different sides of the equation.(Otherwise, you'll have to use implicit differentiation to take the derivative of the equation with both variables in it. On the other hand, clearing the denominator will avoid using Quotient Rule, if you're comfortable with implicit differentiation.)) 3. Popcorn kernels popping can be approximated by a continuous random variable in a probability distribution function. The chance that a popcorn has popped by time t is given by the pdf p t = t e .5 t for t > 0. 2 A. What percent of the popcorn had popped in the first 2 minutes? B. How much of the popcorn popped between minutes 2 and 3? C. What percent of the popcorn unpopped remained after just one minute? D. How long does it take until 99% of the popcorn is popped? 4. Find the area of the regions bounded by the curves x 3 2 y =e 1 and 3 x 2 x 3 x . 5. The Cobb-Douglas productivity function for a particular company is Y L , K =100 L 0.3 K 0.7 where Y is the productivity for K units of capital and L units of labor. When L = 650 and K = 400, which factor has the higher marginal productivity? (Which one, when you increase it, will bring about the greater increase in productivity?) Show your work. 6. Use the definition of the derivative for the following questions. A. State the definition of the derivative of the function f(x): B. Use the definition to find the derivative of the function f x = x 2 9 C. Use your answer from part B to find the equation of the tangent line at x = 5. D. Where does this function have a horizontal tangent? 7. We don't have any method to find the area under the curve y= 40 from x = -2 to x = 0, so we x 4 2 will have to estimate the area. A. Use R4 to estimate this area. B. What determines if R4 is an over-estimate or an under-estimate? C. What is the maximum error for this estimate? D. Give the actual area, rounded to the nearest hundredth. E. How many partitions or rectangles would you need to use to calculate the area to the nearest hundredth. (The maximum error would be 0.01.) (Since Related Rates was an optional section of the curriculum, problem #2 is a bonus problem. I pledge that I have neither given nor received help on this test. _______________________________ (sign) (date)
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Boise State - MATH - 160
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Boise State - MATH - 160
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Boise State - MATH - 160
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Boise State - MATH - 160
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Boise State - MATH - 160
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Boise State - MATH - 160
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Boise State - MATH - 160
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Boise State - MATH - 160
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Boise State - MATH - 160
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Boise State - MATH - 160
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Boise State - MATH - 160
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Boise State - MATH - 160
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Boise State - MATH - 160
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