M215 REVIEW

1. Evaluate two‑sided and one‑sided limits. Problems: p. 79, 89.

2. Determine where a function is continuous or discontinuous and classify the

discontinuities. Problems: p. 110.

3. Find and simplify derivatives by use of definition, product rule, quotient rule, power

rule, chain rule, and implicit differentiation. Sketch the graph of the derivative of a

function by hand and by use of a calculator. Find equations for tangent lines. Use the

derivative to determine the rate of change of one variable with respect to another.

Problems: p. 132, 142, 154, 166, 174,181, 188, 195.

4. Solve related rate problems. Problems: 202.

5. Given the graph of a function, find and classify any maximum and minimum values of

the function. Find the absolute maximum and absolute minimum for a function defined

on a closed interval. Find the critical numbers for a function. Problems: p. 229.

6. State, illustrate, and verify Rolle's Theorem and the Mean Value Theorem (for

derivatives). Determine if a function satisfies the hypothesis of the Mean Value

Theorem or Rolle's Theorem. Problems: p. 238.

7. Sketch and analyze the graph of a function by use of the first and second derivatives by

hand. Specifically, find the intervals over which the function is increasing/decreasing

and those over which it is concave upward/concave downward and find critical points,

points of inflection, and maximum or minimum values. Problems: p: 247.

8. Evaluate limits at infinity. Problems: p. 260

9. Use a calculator to sketch the graph of a function and its first two derivatives and use

the graphs of the derivatives to find the intervals of increase, decrease, extreme values,

intervals of concavity, and points of inflection when given information about the

derivatives. Problems:: p. 277.

10. Solve optimization problems. Problems: p. 283.

11. Compute antiderivatives. Find a function when given its first or first and second

derivatives. Find the position function for a particle when given the velocity or velocity

and acceleration of the particle. Problems: p. 305.

12. Approximate the area under a curve by use of rectangles and right endpoint, left

endpoints or midpoints by hand and by calculator. Problems: p. 324.

13. Approximate definite integrals by calculating Riemann sums by hand and by

calculator. Express limits of Riemann sums as definite integrals. Evaluate definite integrals by

interpreting the integrals in terms of area. Problems: p. 336.

14. Evaluate definite integrals by using the Fundamental Theorem of Calculus Part II. Use

the Fundamental Theorem of Calculus Part I to evaluate derivatives. Compute

indefinite integrals. Prove both parts of the Fundamental Theorem of Calculus.

Problems: p.347, 356 .

15. Compute indefinite integrals and definite integrals by use of substitution.

Problems: p. 365

16. Sketch the region between two curves and find the area. of the region. Problems:

p. 380.

17. Find the volume of a solid of rotation by using disks and cylindrical shells. Find the

volume of a solid of known cross-sectional area. Problems: p. 391, 396.

18. Solve "work" problems. Problems: p. 401.

19. Find the inverse of a function. Problems: p. 420.

20. Find derivatives of expressions involving the natural logarithmic function and use the

natural logarithmic function to evaluate integrals . Problems: p. 458.

21. Evaluate derivatives and integrals involving the natural exponential function.

Problems: p. 465.