# Calculus II

Our online Calculus II tutoring is a continuation of the study of Calculus. It includes further exploration of derivatives of exponential, logarithmic, inverse, and hyperbolic functions. It extends the abilities to integrate more various forms of expressions and investigates techniques of Integration. Online Calculus II explores indeterminate forms and improper integrals leading into Infinite Sequences and Series. The Calculus II course finishes with Analytic Geometry in the Plane.

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All Calculus II Lessons Include

- Logarithmic and Exponential Functions
- Inverse Functions
- The Natural Logarithmic Function
- The Exponential Function
- Integrals Involving Logarithmic and Exponential Functions
- Exponential and Logarithmic Functions to Other Bases
- The Natural Logarithmic Function – A Historical Approach
- The Hyperbolic Functions

- Inverse Trigonometric and Hyperbolic Functions
- Inverse Trigonometric Functions
- Derivatives and Integrals That Involve Inverse Trigonometric Functions
- Inverse Hyperbolic Functions

- Techniques of Integration
- Algebraic Substitutions
- Integration By Parts
- Integration of Powers of Trigonometric Functions
- Trigonometric Substitutions
- Partial Fractions; Denominators Containing Linear Factors; Denominators Containing Irreducible Quadratic Factors
- Integral Tables, Calculators and Computers.

- Intermediate Forms and Improper Integrals
- L' Hopitals Rule
- Indeterminate Forms
- Improper Integrals; Infinite Limits of Integrals; Integrals With an Integrand That Becomes Infinite

- Sequences and Series
- Sequences
- Monotonic Sequences
- Infinite Series
- The Integral and Comparison Tests
- The Ratio and Root Tests
- Alternating Series and Absolute Convergence
- Power Series
- Differentiation and Integration of Power Series
- Taylor Series
- Binomial Series.

- Analytic Geometry In the Plane
- Parabola
- Ellipse
- Hyperbola
- Translation and Rotation of Axes

- Parametric Equations and Polar Coordinates
- Parametric Equations
- Slope of Tangent Lines; Arc Length
- Polar Coordinate System
- Graphs of Polar Equations
- Area in Polar Coordinates; Arc Length
- Conic Sections Revisited