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Calculus Topics

Limits

Finding limits from graphs

Continuity

Finding limits algebraically - direct substitution

Finding limits algebraically - when direct substitution is not possible

Infinite limits - vertical asymptotes

Limits at infinity - horizontal asymptotes

Intermediate value theorem

Squeeze theorem

Limit laws

Derivatives

Definition of derivative

Power rule

Slope and equation of tangent line

Chain rule

Derivative of trigonometric functions

Derivative of exponential functions

Product rule

Quotient rule

Implicit differentiation

Derivative of inverse trigonometric functions

Derivative of logarithmic functions

Higher order derivatives

Derivative Applications

Position velocity acceleration

Critical number & maximum and minimum values

l'Hospital's rule

Curve sketching

Optimization

Related rates

Rolle’s theorem

Mean value theorem

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

Integrals

Antiderivatives

Riemann sum

Definite integral

Fundamental theorem of calculus

Integration Techniques

U-Substitution

Integration by parts

Integration using trigonometric identities

Trigonometric substitution

Integration of rational functions by partial fractions

Improper integrals

Integration Applications

Areas between curves

Volumes of solids with known cross-sections

Volumes of solids of revolution - Disc method

Volumes of solids of revolution - Shell method

Average value of a function

Arc length

Consumer and producer surplus

Continuous money flow

Differential Equations

Order and solutions to differential equations

Separable equations

Modeling with differential equations

Sequence and Series

Introduction to sequences

Monotonic and bounded sequences

Introduction to infinite series

Convergence and divergence of normal infinite series

Convergence & divergence of geometric series

Convergence & divergence of telescoping series

Divergence of harmonic series

P Series

Alternating series test

Divergence test

Comparison & limit comparison test

Integral test

Ratio test

Root test

Absolute & conditional convergence

Radius and interval of convergence with power series

Functions expressed as power series

Taylor and maclaurin series

Approximating functions with Taylor polynomials and error bounds

Parametric Equations and Polar Coordinates

Defining curves with parametric equations

Tangent and concavity of parametric equations

Area of parametric equations

Arc length and surface area of parametric equations

Polar coordinates

Tangents of polar curves

Area of polar curves

Arc length of polar curves

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