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101-1999&amp;2000-3-M20-July2000

# 101-1999&amp;2000-3-M20-July2000 - ~ ~ Kuwait...

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Kuwait University Math. Camp. Sci. Dept. Math 101 Second Exam July 20th, 2000 Time: 75 minutes ~.//' ~-" Calculators and Mobile Phones are not allowed. 1. Let y = tane. a) Use differentials to find dy if e changes from 45° to 44°. b) Us€ a linear approximation to estimate tan 440. (3 Points) 2. As a right circular cylindrical metal rod is being heated, its height is increasing at a rate of 0.002 Cln/min and its radius is increasing at a rate of 0,001 cm/min. At what rate is the volume changing when the rod has height 20 cm and radius 4cm. (3 Points) 3. a) State the mean value theorem. b) Use the mea.n value theorem to show that if It a.nd v are any real numbers, then (3 Points) 4. Find two real numbers whose difference is 10 and their product. is minimum. (3 Points) 5. Evaluate the following integrals: " J 2t - 5 dt, a) .(It x2 6. Let I(x) = 4 _ x2' J 1 b dx ) sin 2x tan 2x . (3 Points) a) Find the vertical and horizontal asymptotes (if any). b)

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101-1999&amp;2000-3-M20-July2000 - ~ ~ Kuwait...

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