9. Improper integrals(a) Use the L'hospital Rule to find the limit of x-² In a when a goes to ∞.In 2Use this result to decide wether the integral ng² du is convergent or divergent. You mustexplain your answer. If the integral ins convergent, then evaluate it.(b) A manufacturer of lightbulbs wants to produce bulbs that last about 700 hundred hours, butof course some bulbs burn out faster than others. Let r(t) denote the rate at which bulbs runout at time t (in hours) and assume r(t) = Ce-0.001t where C is some constant.(1) What is the meaning and value of for(t)dt?(2) Deduce from this the value of the constant C.-700(3) Evaluater(t)dt and explain the meaning of this result.(c) Use the comparison test to prove that the integral ₁+2+1da is convergent.

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Answered: 9. Improper integrals (a) Use the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose f and all of its derivatives are continuous for all x. You are also given the following values: f(0) = 9, f'(0) = -2, f"(0) = 18, f'(0) = 16 Calculate the following limit or determine it does not exist. 18 - 4x - 2f(x) 1- cos(4x) L= lim O A. L= Enter an exact number only. O B. L does not exist.
Consider the function f(x) = * +7. 4 x2 +7) dx by using the definition 3 In this problem you will calculate 9. n f(x) dx = lim 2 f(x;)Ax i=1 The summation inside the brackets is R, which is the Riemann sum where the sample points are chosen to be the right-hand endpoints of each sub- interval. Calculate R, for f(x) = * +7 on the interval [0, 4] and write your answer as a function of n without any summation signs. lim Rp n→00
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