Math 151 Week in Review week 12 5.7, 6.1, 6.2 Spring 2009 The rest of Chapter 6 will be covered in the Final Exam Review.

1. Find the most general antiderivative of each function

a) b) c) d)

2. Find F(x).

a) b)

c) d)

e)

3. #80 pg 355 of Stewart. A projectile is fired with an initial speed of 500 m/s at an angle of elevation of 30 degrees from a position 200 m above the ground. Find a) the trajectory of the projectile, b) the maximum height reached and c) the speed when it hits the ground.

4. #70 pg 355 Stewart. A car is traveling at 50 mi/hr when the brakes are fully applied, producing a constant deceleration of 40 ft/s/s. What is the distance covered before the car comes to a stop?

5. # 72 pg 355 of Stewart. A car braked with a constant deceleration of 40 ft/s/s producing, skid marks

measuring 160 ft. before coming to a stop. How fast was the car traveling when the brakes were first applied?

6. #82 pg 359 Stewart. In an automobile race along a straight road, car A passed car B twice. Prove that at some time during the race their accelerations were equal.

Chapter 6, 6.1-6.3

7. Evaluate each expression.

a) b) c) d) e)

8. Find the right and left hand Riemann sums for on [0, 2] using 4 equal subintervals.

Find the average of these two sums.

9. Find the left hand Riemann sum for on [0, 3] using 20 equal subintervals.

10. Find the left and right hand Riemann sums for f(x) = x on [ -1, 4] using 12 equal subintervals. Use geometry to find the limit of the Riemann sums as the number of subintervals approaches infinity.

11. Find in each case.

a) [a, b] = [0 , 2]

b) f(x) of part a above, a=2, b=0.

c) [a, b] = [-4, 4]

d) [a, b] = [0, 2]

12. For the function of 11 c above, find the area between f(x) and the x-axis for x between 0 and 2.

13. Given that , , find each of the following:

a) b)