Calculus II Competencies

These are competencies with sample problems.

 For mastery of the material you need to work all the assigned homework, not just these problems.

Chapter 7

1) Finding derivative of exponential functions (37p431, 43p432)

2) Constructing exponential models and their rates (Exp. Work.)

3) Applications using exponential curves (Exp. Work.)

4) Integration of exponential functions (77p433)

5) Solving exponential and logarithmic equations (31,35p439)

6) Finding derivatives of logarithmic functions (5,11,35 p449)

7) Applications of logs (Exp. Work.)

8) Logarithmic differentiation (45p450)

9) Evaluate Integrals that give logarithmic functions (69p450)

10) Evaluating trig and inverse trig functions (1,3,5,13p483)

11) Derivatives and integrals of inverse trig functions (31,49P484, 65P485)

12) Modeling with trig and inverse trig functions (Inverse Work)

13) Hyperbolic Functions (3,20p491; 31,53,59p492)

14) Finding limits of indeterminate forms (17p501,51,53,57p502)

15) Finding volumes of revolutions by the method of Disks and Shells (81p433,79p450,72p485)

Chapter 8

1) Integration by Parts (25,27p516; 59,61p517)

2) Trigonometric Integrals (11,27,29,37p524; 61,63p525)

3) Trigonometric Substitutions (7,9p 530; 25p531)

4) Integration by Partial Fractions (11,19p540)  (Partial Fractions Worksheet)

5) Strategies for Integration (33p456; 61,77p 457; Basic Integration Worksheet; Integration Worksheet )

6) Improper Integrals (13,21,37,49,53p574)

Chapter 9

1) Finding the arc length of a curve (7,11,15p588)

2) Find the centroid of a planar region (25,29,33 p606)

Chapter 10

1) Show that a given function is a solution of a DE. (1,5 p627; )

2) Solve the initial value problems using separation of variables               ( 11,19,27 p643)

3) Modeling with DEs (DE Work)

Chapter 11

1) Sketch the graphs of a parametric equations ( 17,21,24p693) Parametric Worksheet

2) Describe the behavior of curves (31-bp694; 43p695) Parametric Worksheet

3) Find an equation of the tangent line to a curve at a given point (7p702) Parametric Worksheet

4) Find points of vertical and horizontal tangent lines ( 17,19p702) Parametric Worksheet

5) Find the arc length of curves described parametrically. (41,43p703) Parametric Worksheet

6) Find the surface area when curves are rotated (59,65p704) Parametric Worksheet

7) Identify polar curves transforming to Cartesian.(19p714; Polar Worksheet)

8) Find polar equations of Cartesian curves (25p714; Polar Worksheet)

9) Identify the graph of basic polar equations (29,31,33,35,37,39,45; Polar Worksheet)

10) Find the slope of a tangent line to a polar curve (55,59p74)

11) Find points of vertical and horizontal tangent lines to polar curves (63,65p714)

12) Find the arc length of polar curves ( 45p720;Polar Worksheet)

13) Find areas in polar coordinates (29,35p719;Polar Worksheet)

14) Describe graph and find equations of conic sections (7,15,23,33,41,47p726;Conics Worksheet)

Chapter 12

1) Find the limit of a sequence. (25, 31p747, Class Notes)

2) Find the sum of a convergent series (11,15,27,33p756)

3) Test the series for convergence /divergence (1-37eoo* p784)

eoo* every other odd (1,5,9,13..)

4) Find the radius/ interval of convergence of power series (9,13,17p789)

5) Represent functions as power series (9,13,25p795)

6) Find the Maclaurin/Taylor series of functions (5,15, Class Notes)

7) Obtain a series from a known series (27p886, 29p807, Class Notes)

8) Evaluate integrals as infinite series (39,40p807)

9) Find the sums of series from known series (55,57p807, Class Notes)

10) Use the binomial series to expand a function as a Maclaurin series (1,3,7p811).