Single Variable Calculus Tags

# Single Variable Calculus Tags

## Limits and continuity

- Finding limits using graphs
- Rules of limits - basic
- Evaluating limits - factoring
- Evaluating limits - rationalizing
- Evaluating limits - rational expressions
- Evaluating limits - trigonometric
- Squeeze theorem
- One-sided limits - concept of
- Continuity - concept of
- Continuity - classifying discontinuities
- Continuity - intermediate value theorem
- Infinite limits and vertical asymptotes
- Limits at infinity, horizontal and oblique asymptotes
- Estimating limits numerically
- Applications - instantaneous rate of change
- Applications - tangent lines and slopes
- Applications - finding all asymptotes
- Applications - other
- Definitions and existence

## Differentiation

- Definition of the derivative
- Conceptual understanding of derivatives
- Derivatives of polynomials and power functions
- Product rule
- Quotient rule
- Derivatives of trigonometric functions
- Derivatives of exponential functions
- Derivatives of logarithmic functions
- Derivatives of inverse functions
- Derivatives of inverse trigonometric functions
- Hyperbolic functions
- Derivatives of hyperbolic functions
- Chain rule
- Higher-order derivatives
- Derivatives involving multiple rules
- Logarithmic differentiation
- Implicit differentiation

## Applications of differentiation

- Mean value theorem
- Rates of change
- Increasing/decreasing functions and local extrema
- Concavity and points of inflection
- Global extrema
- Summary of curve sketching
- Optimization
- Linear approximation and differentials
- Related rates
- Indeterminate forms and L'Hopital's rule
- Newton's method
- Elasticity of demand

## Integrals

- Conceptual understanding of integration
- Antiderivatives
- Indefinite integrals
- Riemann sums
- Definite integrals
- Fundamental theorem of calculus
- Improper integrals

## Techniques of integration

- Substitution
- Integration by parts
- Trigonometric integrals
- Hyperbolic functions
- Partial fractions
- Trigonometric substitution
- Tables of integrals
- Computer algebra system
- Mixed techniques
- Challenging integrals
- Approximation

## Applications of integration

- Average value of a function
- Areas between curves
- Volumes by slices
- Volumes by disks
- Volumes by washers
- Volumes by cylindrical shells
- Volumes by multiple methods
- Arc length
- Surfaces of revolution
- Distance, velocity, acceleration
- Work
- Hydrostatic pressure
- Center of gravity
- Other physics and engineering applications
- Economics
- Biology
- Probability and statistics

## Infinite sequences and series

- Limit of a sequence
- Series notation
- Partial sums
- Taylor polynomials
- Geometric
- Test for divergence
- Comparison tests
- Integral test
- Ratio test
- Root test
- Alternating series test
- Absolute and conditional convergence
- Strategy for testing series
- Interval of convergence of a power series
- Maclaurin series
- Taylor series
- Power series
- Representations of functions as series
- Applications of Taylor polynomials
- Fourier series

## Parametric

- Curves
- Eliminating the parameter
- Tangents, velocity, and speed
- Higher order derivatives
- Arc length
- Area
- Volumes of revolution
- Surface area of surfaces of revolution

## Polar

- Similar figures (Trigonometry, geometric and algebraic foundations for trigonometry, similar figures)
- Polar and rectangular coordinates (Trigonometry, polar coordinates and vectors polar and rectangular coordinates
- Curves (Trigonometry, polar coordinates, vectors, curves)
- Inequalities (Trigonometry, polar coordinates, vectors inequalities)
- Tangents
- Area
- Arc length
- Other applications