Mth252 Final Exam Review Ch4.2,4.3,4.5,4.6,4.9,5.1-5.6,5.7-5.10,6.1-6.5
- Find the absolute maximum and minimum values of on [35,0].
Use the closed interval method. Verify graphically. Sketch the graph.
- Find the local maxima and minima of on . Use the second derivative test. Verify graphically. Sketch the graph.
- Use the graph of f to estimate the values of c that satisfy the MVT on [ 0,5].
- Use L’Hospital’s Rule to evaluate the limits.
a) b) c)
- Find the point on the hyperbola xy=8 that is closest to the point (3,0)
- A man launches his boat from point A on a straight river, 3 km wide, and wants to reach point B, 8 km downstream on the opposite bank. He needs to get there as quickly as possible. He is able to row 6 km/hr and run 8 km/h. What is the least amount of time it will take him to make the trip? (hint: he has 3 options)
- The velocity graph of a braking car is shown. Use it to estimate the distance traveled by the car while the brakes are applied. Estimate using right endpoints, left endpoints, midpoints, Trapezoid Rule, and Simpson’s Rule
8. Water is leaking out of a tank at a rate of gallons/hour, where t is measured in hours. Write a definite integral that expresses the total amount of water that leaks out in the first two hours.
9. Use the Substitution Rule to find the antiderivatives or evaluate the definite integrals.
a) b) c)
10. Use Integration by Parts to find the antiderivatives. Evaluate the definite integral.
a) b) c)
11. Use limits to determine convergence or divergence. Evaluate.
a) b) c)
12. Find the area of the region bounded by y and .
13. Find the volume of the solid of revolution.
a) and about the y-axis
b) about the line x=2
c) about y-axis
d) about x-axis
- Find the exact and approximate length of the arc
- Suppose a study indicates that t years from now, the level of carbon dioxide in the air of Portland will be parts per million (ppm). a) What is the average level of carbon dioxide in the first 3 years? b) At what time (or times) does the average level of carbon dioxide actually occur? Answer to the nearest month.
- A cylindrical tank of radius 8 feet is half full of oil (weight density 50 lb/ft). Find the work required to pump all of the oil through a hole in the top of the tank. The height of the tank is 15 feet.
- An object located x ft from a fixed starting position is moved along a straight road by a force of lb. What work is done by the force to move the object from 1 ft to 4 ft?
1 of 1m252finalr_sp04 p.siekas