Subjective Short Answer 1. Find if . ​ 2. Find an equation of the tangent line to the graph of at the point . ​ 3. Evaluate the using L’Hà´pital’s Rule if necessary. 4.

Use the differential equation and the initial condition to find y. Objective Short Answer 5. Evaluate the definite integral. 6. Find the following indefinite integral. ​ ​ 7.

Evaluate the limit using L'Hopital's Rule if necessary. 8. Find an equation of the tangent line to the graph of at the point . 9. Evaluate the integral .

Name: Class: Date: 2414 Group Activity Midterm Review 10. Find the area of the region bounded by the graphs of the algebraic functions. ​ ​ 11. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x- axis. , , , 12. Use the shell method to set up and evaluate an integral that gives the volume of the solid generated by revolving the plane region about the y-axis. , 13. Use the shell method to find the volume of the solid generated by revolving the plane region bounded by , , about the line .

14. Find the arc length of the graph of the function over the interval . 15. Set up and evaluate the definite integral for the area of the surface formed by revolving the graph of , about the x-axis. 16.

Find the indefinite integral. ​ ​ 17. Find the indefinite integral. ​ ​ Name: Class: Date: 2414 Group Activity Midterm Review 18. Evaluate the definite integral . ​ 19. Find the indefinite integral. 20.

Find the indefinite integral. 21. Use partial fractions to find . 22. Use partial fractions to find the integral .

23. Use integration tables to evaluate the integral . 24. Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

25. Find the derivative of the function . 26. Find the indefinite integral. ​ ​ 27. Solve the following equation for . ​ ​ Name: Class: Date: 2414 Group Activity Midterm Review 28.

Find if . ​ 29. Evaluate the limit first by using techniques from Chapter 1 then by using L'Hopital's Rule. 30. Evaluate the limit using L'Hopital's Rule if necessary. 31.

Evaluate the limit using L'Hopital's Rule if necessary. 32. Evaluate the expression without using a calculator. 33. Find the derivative of the function .

34. Find the integral . 35. Find the indefinite integral. Name: Class: Date: 2414 Group Activity Midterm Review 36.

Find the area of the shaded region for the function . 37. Find the area of the region bounded by the equations by integrating (i) with respect to x and (ii) with respect to y. ​ ​ 38. Find the area of the region bounded by the graphs of the equations. ​ , , ​ 39. Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by and in the first quadrant about the y-axis.

Name: Class: Date: 2414 Group Activity Midterm Review 40. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line . 41. Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. , , 42. Use the disk or shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line . , , , 43.

Find the arc length of the graph of the function over the interval . 44. Find the area of the surface generated by revolving the curve about the x-axis. , . 45. Find the arc length of the graph of the function over the interval .

Name: Class: Date: 2414 Group Activity Midterm Review 46. Set up and evaluate the definite integral for the area of the surface formed by revolving the graph of about the y-axis. Round your answer to three decimal places. ​ 47. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given lines. ​ (i) x-axis; (ii) the line 48. Find the integral 49.

Find the slope-intercept form of the equation of the line tangent to the graph of when . 50. Write the following expression in algebraic form. Name: Class: Date: 2414 Group Activity Midterm Review Answer Key 1. 2.

3. 0 4. 5. 6. 7.

1 8. 9. 10. 11. ​ 12. ​ 13. 14.

15. 16. Name: Class: Date: 2414 Group Activity Midterm Review 17. 18. . 20. ​ 21.

22. 23. 24. diverges 25. 26. 27.

28. 29. . 31. . 33. 34.

Name: Class: Date: 2414 Group Activity Midterm Review 35. 36. 37. 38. 39.

40. ​ 41. ​ 42. ​ 43. 44. ​ 45. 46. 36.. ​ 48. Name: Class: Date: 2414 Group Activity Midterm Review