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Introduction to Calculus - Limits

Finding limits from graphs

Limit Laws

Finding limits algebraically - direct substitution

Finding limits algebraically - when direct substitution is not possible

Squeeze Theorem

l'Hospital's Rule

Infinite limits - vertical asymptotes

Limits at infinity - horizontal asymptotes

Continuity

Intermediate value theorem

Definition of derivative

Estimating derivatives from a table

Power rule

Chain rule

Derivative of trigonometric functions

Derivative of exponential functions

Derivative of logarithmic functions

Product rule

Quotient rule

Derivative of inverse trigonometric functions

Implicit differentiation

Higher order derivatives

Slope and equation of tangent line

Critical number & maximum and minimum values

Curve sketching

Rolle's theorem

Mean value theorem

Rectilinear motion: derivative

Related rates

Optimization

Linear approximation

Quadratic approximation

Demand, revenue, cost & profit

Marginal revenue, and maximizing revenue & average revenue

Marginal cost, and minimizing cost & average cost

Marginal profit, and maximizing profit & average profit

Elasticity of demand

Continuous compound interest

Antiderivatives

Riemann sum

Definite integral

Fundamental theorem of calculus

U-Substitution

Integration using trigonometric identities

Trigonometric substitution

Integration by parts

Integration of rational functions by partial fractions

Numerical Integration

Average value of a function

Area between curves

Volume of solids with know cross-sections

Volume of solids of revolution - Disc method

Volume of solids of revolution - Shell method

Consumer and producer surplus

Continuous money flow