practice_prelim1_fa06 - Practice Prelim 1, Math 191, Fall...

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Practice Prelim 1, Math 191, Fall 2006No calculators. Show your work. Clearly mark each answer.This practice prelim may be longer than the actual prelim.1. The max-min inequality for definite integrals is helpful in the following.[10](a) Find upper and lower bounds for20x1 +x2dx .(b) Rewrite the integral of part (a) by using the substitutionu=x2. Find upper and lower boundsfor the resulting integral.2. Write the sumnk=1n3+k3n4as a Riemann sum in order to evaluatelimn→∞nk=1n3+k3n4.[10]3. Evaluate:[20](a)1-1tcos(sint)dt(b)ddy4y0sintcost dt(c)3v-1dv(d)t1-4t2dt4. Consider the region described byy1
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Term
Spring
Professor
BERMAN
Tags
Definite Integrals, Integrals, lower bounds, Practice Prelim

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