Name Applied Calc. 2 Homework Please show all your work Answers must be supported . Good luck! Due February 28th by 11:59 pm. EST 1. Given y x 3 and y x 2 , find the area between both curves. 2. Solve the separable Differential Equation 2 dy y ( x 1)dx . Remember to do your best for solving for y here. For the sake of keeping things simple, assume that everything is positive. 3. Determine whether the integral is convergent or divergent. dx. If convergent, then x xe dx 0 evaluate. 4. Determine whether the integral is convergent or divergent. . If convergent, then x 5 dx 1 evaluate. 5. Solve the separable Differential Equation r(0)=2. dr r (q 4 q 2) dq , with the initial condition of 6.(Each part is worth 10 points) Suppose the average wait to eat at Denny's is four minutes. A. Find the probability that you will be called in the first two minutes of your wait. B. Find the probability that the wait is greater than four minutes. 7. Use the midpoint rule with four subintervals to estimate the value of . 4 ln( x 2 x 2)dx 0 8. Find the consumer surplus for the given demand function and sales level.(Hint: Look at Example 1 in Section 6.2) q p 6 , 3500 12,000 9. Find the area between the two curves. and y 8 x 1 y x3 4 10. Given the fact that and that b P(a x b) f ( x)dx z . This means that all f ( x)dx 1 probabilities lie between 0 and 1. Show that 2 f ( x) kx (1 x) if 0 x 1 and f ( x) 0 if value of k is f a probability function. (Show all your steps) x0 and if x 1 . For what