1. [-/3 Points] DETAILS MY NOTES Find the average value of the function f(x) = x + 9x + 8 on [0, 2]. 2. [-/4 Points] DETAILS MY NOTES Find the average value of the function ((x) = x In(x?) + 3 on [e, e~]. Hint: " (x In(x) - x) = In(x). 3. [-/5 Points] DETAILS MY NOTES Find two values of c in _ such that f(c) is equal to the average value of /(x) = 3 cos(2x) on -. . (Round your answers to three decimal places. Enter your answers as a comma separated list.) 4. [-/4 Points] DETAILS MY NOTES Find a value c in [1, 5] such that Ac) is equal to the average value of /(x) = e"+ 1 on [1, 5]. (Round your answer to three decimal places.)5. [-/4 Points] DETAILS MY NOTES Consider the following step function. u(x ) = x50 Calculate the average value of u(x) on [-1, 1]. Is there a value c in [-1, 1] such that u(c) attains the average? If not, why does the mean value theorem for integrals fail? O No, there is no such value of c because u(x) is not continuous on [-1, 1]. No, there is no such value of c because u(x) is not integrable on [-1, 1]. O Yes, u(c) attains the average value at c = 0. Yes, u(c) attains the average value at c = 0.5. Yes, u(c) attains the average value at c = 1. 6. [-/8 Points] DETAILS MY NOTES A colony of bacteria has a total weight which varies according to w(t) = 16.5e-35 (weight in Newtons, time in hours). Find the average weight of the colony over the interval [1, 5]. (Round your answer to two decimal places.) N Find a value c in [1, 5] such that w(c) attains this average. (Round your answer to two decimal places.) c = hr 7. [-/5 Points] DETAILS MY NOTES Di's velocity, in miles per hour, & minutes after entering the interstate highway is given below. v(t) = - 200 20' 1 3 4 3+2 - 3r + 60 t s 30 What was Di's average velocity, in miles per hour, from the interval t = 5 min to t = 20 min? (Round your answer to two decimal places.) mph 8. [-/6 Points] DETAILS MY NOTES The temperature over a 10-hour period in December in St. Paul, Minn., is given below. T(t) = -12 + 3t + 30 ost= 10 Find the average temperature, the minimum temperature, and the maximum temperature. (Round your answers to two decimal places.) average temperature minimum temperature maximum temperature