CALCULUS 2: FINAL REVIEW SHEET

Be able to take all previous tests without error

• Section 5.5 The Substitution Rule
• Examples New Book p. 381 # 13,32,34,36,45
• Section 5.6 Integration by Parts

-Choose u by LIATE!

-Examples p. 387 #3,7,10,16

Section 5.7 Additional Techniques of Integration

-Trig Integrals Exercises1,2,4,5,6 from here

-Trig Substitution Exercises 1,2,3,17 from here

• Appendix G- Integration with Partial Fractions

-Look at the Appendix G worksheet, ex A54 7,9,11,21

Section 5.9 Approximate Integration

-Know both the Trapezoidal Rule and Simpson’s Rule

-Examples p. 411 #3,6

• Section 5.10 Improper Integrals

-Be able to determine whether an improper interval is convergent or divergent

-Examples p. 421 # 1,5,25

Section 6.1 More About Areas

-Be able to graph the region enclosed by the given curves & find its area

-Examples p. 436 # 7,9,13

• Section 6.2 Volumes

-Be able to find volumes using washers or disks

-Examples p. 446 # 5,7,17 See Volumes Worksheet

• Section 6.6 Applications to Physics and Engineering

-Spring Problems (Know Hooke’s Law and how to find Work) p.473 #5,7

- Hydrostatic Force Worksheet

-Work emptying a tank p. 473 17,19, 21

• Section 7.3 Separable Equations

-Separable equations p. 514 # 1,3,13

-Orthogonal Trajectories p. 514 # 29,31

-Mixing Problems p. 515 #45,48 See Mixing Problems Worksheet

• Section 7.4 Exponential Growth and Decay

- p. 527 # 1,3,5,9

• Section 7.5 Logistic Equation

- p. 538 # 1,7

• 7.7 Second Order Linear Differential Equations

http://stewartcalculus.com/data/CALCULUS%20Concepts%20and%20Contexts/upfiles/3c3-2ndOrderLinearEqns_Stu.pdf -Examples #1, 3,5,7,17,25

-Know how to find solutions to the auxiliary equation of ax’’+bx’+cx=0 for all 3 cases.

-Be able to solve initial and boundary value problems.

• 7.8 Nonhomogeneous Linear Equations http://stewartcalculus.com/data/CALCULUS%20Concepts%20and%20Contexts/upfiles/3c3-NonhomgenLinEqns_Stu.pdf

-Be able to find the complementary solution

-Find the particular solution using the Method of Undetermined Coefficients

-Use the complementary and particular to find the general solution

- Examples #1-17 odd (Note: #13, 15,17 don’t require you to find the values of the coefficients) Look at 7.7/7.8 Worksheet

• 7.9 Applications of Second-Order Differential Equations

http://stewartcalculus.com/data/CALCULUS%20Concepts%20and%20Contexts/upfiles/3c3-AppsOf2ndOrders_Stu.pdf

-Be able to use the techniques from 7.7 and 7.8 to solve problems involving springs.

-Examples 1,3,5, 7 Notice: These are easier than some of the problems we’ve worked in class

• 8.1 Sequences

-Examples p. 562 #1,11, 15,

• 8.2 Series

-Be able to determine if a given series is convergent

-Know when a geometric series is convergent and what it converges to p. 569

-Know about the Harmonic Series

-Know the Test for Divergence

-Examples p. 572 #1,9, 11,15,19,25Sequences and Series Worksheet

• 8.3 The Integral and Comparison Tests; Estimating Sums

-Know when the Integral test, Comparison Test, Limit Comparison test can be applied.

-Know when a p-series converges and when it diverges

-Examples: p. 583 # 3,13, 17, 21 Comparison Test Worksheet

• 8.4 Series Other Convergence Tests

-Know the Alternating Series Test, the Ratio Test

-Examples: p. 591 #3,5,7,21,23,37

-Know the Test for Divergence

• 8.5 Power Series

-Be able to find the radius and interval of convergence for a given Power Series & be able to justify your work

-Examples: p. 597 # 3,13,15

• 8.6 Representations of Functions as Power Series

-Understand how to use the Geometric series to represent a Power series

-Examples: p. 603 # 5, 7,13

• 8.7 Taylor and Maclaurin Series
• -Know the difference between a Taylor and Maclaurin series.

-Be able to use a Taylor polynomial to approximate different values (p. 625 #3,5,7 and the problems we’ve worked in class)

-Examples: p. 616 # 5,7,9,11,25,,43,59,63