1. Calculate or estimate limits of functions given by formulas, graphs, or tables.

 

2. Determine whether a function given by a graph or formula is continuous at a given point or on a given interval or on its domain.

 

3. Determine whether a function given by a graph or formula is differentiable at a given point or on a given interval.

 

4. Distinguish between average and instantaneous rate of change and interpret the definition of the derivative graphically.

 

5. Determine derivatives of some functions using the limit definition of the derivative.

 

6. Calculate derivatives of polynomial, rational, and common transcendental functions, and combinations of these functions.

 

7. Calculate derivatives of composite functions.

 

8. Calculate derivatives of implicitly defined functions.

 

9. Apply the ideas and techniques of derivatives to related rate problems.

 

10. Give examples to illustrate important theorems. (Intermediate Value Thm, Rolle’s Thm, Mean Value Thm, Extreme Value Thm, Squeeze Thm)

 

11. Apply the ideas and techniques of derivatives to finding local and absolute extrema.

 

12. Apply the ideas and techniques of derivatives to graphing functions.

 

13. Apply the ideas and techniques of derivatives to optimization problems.

 

14. Find linear approximations of functions (differentials).

 

15. Calculate the Riemann sum for a given function and partition.

 

16. Describe a definite integral as the limit of a Riemann sum.

 

17. Determine antiderivatives of some algebraic functions and some trigonometric functions.

 

18. Calculate values of definite integrals using antiderivatives and areas.

 

19. Use the Fundamental Theorem of Calculus to determine the derivative of an integral.

 

20. Use the Fundamental Theorem of Calculus to evaluate definite integrals.

 

21. Apply substitution techniques to integrate functions.

 

22. Apply the ideas of definite integrals to calculate the area of a region between curves.

 

23. Differential Equations

 

24. Apply the ideas of definite integrals to calculate the volume of a solid of revolution rotated about a coordinate axis.

 

25. Apply the ideas of definte integrals to calculate the volume of a solid of revolution rotated about a line parallel to a coordinate axis.