Please #1, 5, 7, 13, 15, 17, 19, 21

18 Find the average value of the function on the given interval. 15. Find the average value of f on [0. 8]. tJm=W+m[4 ZWFJM] 3. g(x) = 3 cos I. [1r/2. 1T/2J elf: 4- f(2)= .. [1.4] 2. 9 5. g(t) = 1 + '2 . [0, 2] 16. The velocity graph of an accelerating car is shown. (a) Use the Midpoint Rule to estimate the average I" velocity of the car during the rst 12 seconds. 6' f\") = (x3 + 3)? [1' I] (b) At what time was theinstantaneous velocity equal to the average velocity? 7. HI) = cos'x sin in [0. 1r] 8. Mn) = 12!" [1.5] 91 2 (a) Find the average value of f on the given interval. (b) Find 6 in the given interval such that f\"g = f(('). (c) Sketch the graph of j and a rectangle whose base is the given interval and whose area is the same as the area under the graph of f. 0 4 8 12 r (seconds) _ 2 17. In a certain city the temperature (in F) t hours after 9' \" _ 1/, ' [1' 3] 9 AM was modeled by the function 10. glx) = (x + 1)". [0. 2] 1n T(t) = 50 + l4sin a 11. for) = 2 sinx sin 2x. L0. 71'] 12 3 12. f (x) = 2x?\" [0 2 J Find the average temperature during the period from 9 AM to 9 PM. 13. If] is continuous and Hf\") dx = 8, show that f takes 18. The gure shows graphs of the temperatures for a city on the East Coast and a city on the West Coast during a 24-hour period starting at midnight. Which city had the highest tem 14. Find the numbers b such that the average value of perature that day? Find the average temperature during this f (x) = 2 + 6x 3x" on the interval [0. b] is equal to 3. time period for each city using the Midpoint Rule with on the value 4 at least once on the interval [1, 3]. n = 12. Interpret your results; which city was \"warmer" overall that day? 4 8 12 I6 20 r (hours) 19. The linear density in a rod 8 m long is lZ/t/x + l kg/m. where x is measured in meters from one end of the rod. Find the average density of the rod. 20. The velocity v of blood that ows in a blood vessel with radius R and length I at a distance r from the central axis is P , 2 v(r)=4m(R -r) where P is the pressure difference between the ends of the vessel and n is the viscosity of the blood (see Example 3.7.7). Find the average velocity (with respect to r) over the interval 0 s r S R. Compare the average velocity with the maximum velocity. 21. In Example 3.8.] we modeled the world population in the second half of the 20th century by the equation PU) = 25606mmm'. Use this equation to estimate the aver age world population during this time period (19502000). 22. (a) A cup of coffee has temperature 95C and takes 30 minutes to cool to 61C in a room with temper ature 20C. Use Newton's Law of Cooling (Sec- tion 3.8) to show that the temperature of the co'ee after t minutes is T(r) = 20 + 753*" where k z 0.02. (b) What is the average temperature of the coffee during the rst half hour? 23. Use the result of Exercise 5.5.89 to compute the average vol- ume of inhaled air in the lungs in one respiratory cycle. 24. If a freely falling body starts from rest. then its displace- ment is given by 5 = %gtz. Let the velocity after a time T be in. Show that if we compute the average of the velocities with respect to twe get a"; = 5-97, but if we compute the average of the velocities with respect to s we get 03.5 = gar. 15. Use the diagram to show that if f is concave upward on [0, b]. then 2627 Let fat; [(1. b] denote the average value of f on the interval [0. b]. 26. Show that ifa