test 4 takehome

test 4 takehome - dV dt =−.05 t If this channel is open...

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Name: ______________ Test #4: Integrals Take-home portion Calculators Allowed. Show the setup for the integrals, but you can use the calculator to evaluate it. 1. A computer running a Microsoft operating system will experience its first Blue Screen Of Death (BSOD) within the first t years given by the probability density function ( t > 0) f t = 4 t t 2 2 2 A. What's the probability that a computer will get its first BSOD between the 2 nd and 4 th year? B. What's the probability that a 10 year old computer won't have gotten a BSOD? C. By what time (exact, or rounded to the nearest hundredth) will half the computers get their first BSOD? 2. Find the area bounded by the curves y = x 3 2 x 2 x 6 and y = x 2 4 5 , rounded to three decimal places.
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3. The amount of water flowing into a holding pool (i.e., the rate at which the volume of the water in the pool is changing) t hours after the channel opens is given by the function dV dt = 100 .5 t 2 2 1 and the amount of water leaving the pool due to evaporation is given by
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Unformatted text preview: dV dt =− .05 t . If this channel is open for 10 hours, what is the total amount of new water in the holding pool? 4. Estimate the area under the curve y = x 2 2 from x = 2 to x = 4 using: A. L 4 B. R 4 C. A Riemann sum S 4 where for each interval [ x k-1 , x k ], let c k = 2 x k − 1 x k 3 D. What is the maximum error bound for these estimates? E. If we wanted to estimate the area to within 0.05, how many intervals will we need? F. What is the actual area? (Do this by hand and show all steps. You can check it with a calculator, but I want to see the work.) G. What is the actual error for each estimate? Error for L 4 : Error for R 4 : Error for S 4 : EC: Find the area bounded from above by the lines y = 1/3 x + 4 and y = -1/2 x + 13/2, and from below by the curve y = x 2 − 5 x 4 I pledge that I have neither given nor received aid on this test. _________________________________ (name) (date)...
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test 4 takehome - dV dt =−.05 t If this channel is open...

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