CALCULUS KHAN ACADEMY PRACTICE MODULES
LIMITS
TAKING DERIVATIVES
- Slope of secant lines
- Tangent slope is limiting value of secant slope
- The formal and alternate form of the derivative
- Derivative intuition
- Recognizing slope of curves
- Graphs of functions and their derivatives
- Visualizing derivatives
- Symbolic differentiation
- Power rule (basic)
- Power rule (advanced)
- Special derivatives quiz
- Special derivatives
- Chain rule on two functions
- Chain rule on three functions
- Product rule
- Quotient rule
- Implicit differentiation
- Derivatives of inverse functions
- Logarithmic differentiation
DERIVATIVE APPLICATIONS
- Applications of derivatives: tangent and normal lines
- Applications of derivatives: motion along a line
- Critical numbers
- Extreme values from graphs
- Extreme value theorem
- Recognizing concavity
- Concavity and the second derivative
- Second derivative test
- Optimization
- Applications of differentiation in biology, economics, physics, etc.
- Related rates
- Mean value theorem
- L'Hopital's rule
- Local linearization
- Tangents to polar curves
INTEGRALS
INTEGRATION APPLICATIONS
SEQUENCES SERIES AND FUNCTION APPROXIMATION
- Understanding sequences
- Geometric sequences 1
- Geometric sequences 2
- Convergence and divergence of sequences
- Arithmetic series
- Understanding series
- Convergence and divergence of series
- Calculating finite geometric series
- Infinite geometric series
- nth term test
- Ratio test
- Direct and limit comparison tests
- Alternating series
- Alternating series remainder
- Creating power series from geometric series using algebra
- Creating power series from geometric series using differentiation and integration
- Maclaurin series for sin x, cos x, and e^x
- Integration and differentiation of power series
- Finding Taylor series