# Calculus Help & Practice

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##### 1Limits

- 1.1Introduction to Calculus - Limits
- 1.2Finding limits from graphs
- 1.3Continuity
- 1.4Finding limits algebraically - direct substitution
- 1.5Finding limits algebraically - when direct substitution is not possible
- 1.6Infinite limits - vertical asymptotes
- 1.7Limits at infinity - horizontal asymptotes
- 1.8Intermediate value theorem
- 1.9Squeeze theorem
- 1.10Limit laws

- 1.1Introduction to Calculus - Limits
##### 2Derivatives

- 2.1Definition of derivative
- 2.2Estimating derivatives from a table
- 2.3Power rule
- 2.4Slope and equation of tangent line
- 2.5Chain rule
- 2.6Derivative of trigonometric functions
- 2.7Derivative of exponential functions
- 2.8Product rule
- 2.9Quotient rule
- 2.10Implicit differentiation
- 2.11Derivative of inverse trigonometric functions
- 2.12Derivative of logarithmic functions
- 2.13Higher order derivatives

- 2.1Definition of derivative
##### 3Derivative Applications

- 3.1Position velocity acceleration
- 3.2Critical number & maximum and minimum values
- 3.3l'Hospital's rule
- 3.4Curve sketching
- 3.5Optimization
- 3.6Related rates
- 3.7Rolle's theorem
- 3.8Mean value theorem
- 3.9Linear approximation
- 3.10Quadratic approximation
- 3.11Demand, revenue, cost & profit
- 3.12Marginal revenue, and maximizing revenue & average revenue
- 3.13Marginal cost, and minimizing cost & average cost
- 3.14Marginal profit, and maximizing profit & average profit
- 3.15Elasticity of demand

- 3.1Position velocity acceleration
##### 4Integrals

##### 5Integration Techniques

##### 6Integration Applications

##### 7Differential Equations

##### 8Sequence and Series

- 8.1Introduction to sequences
- 8.2Monotonic and bounded sequences
- 8.3Introduction to infinite series
- 8.4Convergence and divergence of normal infinite series
- 8.5Convergence & divergence of geometric series
- 8.6Convergence & divergence of telescoping series
- 8.7Divergence of harmonic series
- 8.8P Series
- 8.9Alternating series test
- 8.10Divergence test
- 8.11Comparison & limit comparison test
- 8.12Integral test
- 8.13Ratio test
- 8.14Root test
- 8.15Absolute & conditional convergence
- 8.16Radius and interval of convergence with power series
- 8.17Functions expressed as power series
- 8.18Taylor and maclaurin series
- 8.19Approximating functions with Taylor polynomials and error bounds

- 8.1Introduction to sequences
##### 9Parametric Equations and Polar Coordinates