1. The average value of y = k(x) is 6 for 1 5 x $ 5, and, the average value is 8 for 5 S x $ 8. What is the average value of k(x) for 1 s x $ 8? 2. Find the average value of fon [0,2] and find the number, c, that satisfies the conclusion of the Mean Value Theorem for Integrals, given f (x) = 2x2 + 3. A. Average Value B. C= 3. Find the value of c guaranteed by the Mean Value Theorem for J, (2 + 3VX ) dx4. Find the cost to produce 75 widgets if the initial cost is $2400 and C'(x) = 120 - 40x + x?. [Calculator] 5. If a tennis ball is dropped from a height of 65 feet, on planet Euler takes 4 seconds to hit the ground, what is the gravity on the planet? 6. A particle is moving along a line so that its velocity is v(t) = 3 - 9t2 + 15t + 10 feet per second at time t. [Calculator] A. What is the displacement of the particle on the time interval 0 S t $ 5? B. What is the total distance traveled by the particle on the time interval 0 s t $ 5 ? 7. The total number of documents Hayden has uploaded to his oogle Drive account is in creasing at a rate of r(t) = 8 - 1.2t files per week, where t is the time in weeks. Explain the meaning of the expression: 8 -1.2t at = 17 8. Students are leaving the stadium after a school football game at a rate of r(t) = 1602 students per minute, where tis measured in minutes. How many students left the football game in the first 10 minutes? [Calculator]9. Find the average value of f (x) = sin x on the interval (0, m]. A. B. 3 C. D. 10. Brian has an online video channel for tutoring physics. The total number of subscribes to Brian's page is changing at a rate of r(t) = 14 + 1.8t subscribers per week where t is the time in weeks. At time t = 7 weeks Brian has 438 subscribers. Which expression can be used to determine how many subscribers Brian has by week 15? A. r(15) B. 438 + [, r(t) dt C. 438 + r(15) - r(7) D. [ r(15) dt 11. The area bounded by the curves of y = x2 - 8 and y = -x? is A. B. C. D. 12. The area bounded by the curves y = cos (),y = sin x, x = = and x = n is A. 2 B. C. 1 D. 13. The volume of the solid generated by revolving the region bounded by the curves y = =, * = 0, y = 1, and y = 3 about the y-axis equals A. 3 B. C. D