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Master Calculus 2

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75 skills · 1,627 questions

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75 core skills 100% total weight

01

Arc Length (Cartesian)

02

Arc Length & Distance Traveled

03

Surface Area of Revolution

04

Area Between Curves (x-functions)

05

Area Between Curves (y-functions)

06

Area Between Multiple Intersections

07

Cross Sections: Squares & Rectangles

08

Cross Sections: Triangles & Semicircles

09

Disc Method: Other Axes

10

Disc Method: x- or y-Axis

11

12

Washer Method: Other Axes

13

Washer Method: x- or y-Axis

14

Accumulation Functions in Context

15

Average Value of a Function

16

Position, Velocity, Acceleration via Integrals

17

18

Modeling with Differential Equations

19

Verifying DE Solutions

20

General Solutions: Separation of Variables

21

Particular Solutions: Initial Conditions

22

Solving Separable DEs

23

Reasoning with Slope Fields

24

Sketching Slope Fields

25

Exponential Growth and Decay Models

26

Logistic Models

27

Accumulation Function Behavior

28

Accumulations of Change

29

FTC & Accumulation Functions

30

FTC & Definite Integrals

31

Integration: Long Division & Completing Square

32

Properties of Definite Integrals

33

Riemann Sum Approximations

34

Riemann Sums & Notation

35

Selecting Integration Techniques

36

Arc Length of Parametric Curves

37

Area Between Parametric Curves

38

Motion with Parametric & Vector Functions

39

Parametric Equations & Derivatives

40

Second Derivatives: Parametric

41

Area Between Two Polar Curves

42

Area of a Polar Region

43

Polar Coordinates & Differentiation

44

Slope & Tangent Lines in Polar

45

Integrating Vector-Valued Functions

46

Vector-Valued Functions & Derivatives

47

Algebraic & Trig Simplification

48

Approximation Error & Bounds

49

Interpreting Graphs for Setup

50

Absolute vs. Conditional Convergence

51

Alternating Series Test

52

Comparison Tests

53

54

nth Term Test for Divergence

55

Radius & Interval of Convergence

56

57

Alternating Series Error Bound

58

Lagrange Error Bound

59

Representing Series as Power Series

60

Taylor & Maclaurin Expansions

61

Taylor & Maclaurin Series

62

Taylor Polynomial Approximations

63

Convergent & Divergent Series

64

Sequence Convergence & Limits

65

Geometric Series

66

Harmonic & p-Series

67

Integrating sin & cos Products

68

Integrating tan & sec Products

69

Trig Substitution

70

Choosing Integration Methods

71

Improper Integrals

72

Integration by Parts

73

Integration by Substitution

74

Linear Partial Fractions

75

Partial Fractions: Repeated & Quadratics