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Calculus 1
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Limits
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History of calculus
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Intro to calc 1
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Intro to continuity
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Continuity
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Finding and classifying discontinuities
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Finding the value that makes the function continuous
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Limits
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Intro to limits
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Tabular and graphical estimation of limits
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Finding one-sided limits from graphs
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Finding one-sided limits
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Limits that do not exist
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Estimating limits from tables
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Lesson
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Practice
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Finding limits at infinity
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Finding basic limits
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Finding limits by simplifying complex fractions
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Finding limits of exponential functions
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Finding limits of rational functions
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Sum of an infinite geometric series
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Koch curve
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Finding limits of trigonometric functions
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Finding one-sided limits of piecewise functions
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Finding limits by factoring
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Finding limits by rationalizing
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Lesson
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Practice
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Finding limits using u-substitution
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Proving the derivative of the natural logarithm
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Epsilon-delta proofs
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Epsilon-delta definition of limits
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Epsilon-delta proof: Product of limits
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Epsilon-delta proof: Sum of limits
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Epsilon-delta proofs for limits with one variable
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Epsilon-delta proofs of uniform continuity
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Epsilon-delta proofs for limits with two variables
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Finding delta given epsilon
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Derivatives: definition and basic derivative rules
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Logarithmic functions
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Leibniz's derivative notation
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Differentiability of a function
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Proving differentiable implies continuous
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Derivative of a function from first principles
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Lesson
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Practice
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Finding the tangent or normal line through the given point
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Constant rule
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Constant multiple rule for derivatives
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Sum, difference, and power rules for derivatives
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Proofs
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Using the theorem
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Intro
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Product rule
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Proving the product rule
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Quotient rule
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Derivatives of trig functions
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Proving properties of even and odd functions (calculus 1)
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Derivatives: composite, implicit, and inverse functions
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Derivative at a point from first principles
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Derivatives of exponential functions
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Derivatives of logarithmic functions
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Derivatives of hyperbolic and inverse hyperbolic functions
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Using the derivatives of the hyperbolic functions
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Proving the derivatives of the hyperbolic functions
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Proving the derivatives of the inverse hyperbolic functions
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Derivatives of inverse trig functions
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Derivatives of transcendental functions
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Derivatives of trigonometric functions under transformations
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Derivative using u-substitution
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Determining derivatives from graphs
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Higher order derivatives
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Chain rule
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Derivatives of inverse functions
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Applying derivatives to analyze functions
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False position method
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L'Hopital's rule
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Applications of trigonometric derivatives
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Extreme value theorem
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First derivative test
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Mean value theorem
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Related rates
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Second derivative test
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Concavity
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Factoring a cubic polynomial with a double root
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Graphing using derivatives
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Special points
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Finding critical values from graphs
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Lesson
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Practice
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Finding critical values using derivatives
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Inflection points
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Graphically finding points of inflection
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Using the second derivative to find points of inflection
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Classifying stationary points
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Sketching polynomials using stationary points
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Bisection method
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Newton's method
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Integrals
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Basic integration problems
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Integration by u-substitution
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Integration by u-substitution (less difficult)
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Lesson
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Practice
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Integration by u-substitution (more difficult)
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Integrating exponential functions by u-substitution
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Visually determining antiderivative
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Applications of integrals
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Proving the formula for the area of a circle
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Area between two curves
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Solids of revolution
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Disc and washer methods (circular cross sections)
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Volumes of solids with known cross sections
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Shell method
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Volume of a sphere (calculus \(2\))
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Volume of a cone (calculus 2)
›
Calculus 1
›
Derivatives: composite, implicit, and inverse functions
›
Derivatives of exponential functions
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