functions 34 videos

Continuous Functions
Calculus Limits and Continuity
How to determine whether a function f(x) is continuous everywhere on its domain.
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The Derivative Function
Calculus The Derivative
How to define the derivative function f'(x).
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Derivatives of Linear Functions
Calculus The Derivative
How to determine the derivative of a linear function.
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Derivatives of Power Functions
Calculus The Derivative
How to determine the derivative of a power function.
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Derivatives of Polynomial Functions
Calculus The Derivative
How to compute the derivative of a polynomial function using two properties of the derivative.
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Derivatives of Exponential Functions
Calculus The Derivative
How to use the definition of the derivative to find a derivative formula for exponential functions.
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Average Value of a Function
Calculus The Definite Integral
How to find the average value of a function over an interval [a,b].
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The Chain Rule
Calculus Techniques of Differentiation
How to differentiate a composite function.
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Chain Rule: The General Power Rule
Calculus Techniques of Differentiation
How to differentiate a composite function when the outside function is a power function.
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Chain Rule: The General Exponential Rule
Calculus Techniques of Differentiation
How to differentiate a composite function when the outside function is exponential.
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Tricky Substitutions Involving Radicals
Calculus Antiderivatives and Differential Equations
How to antidifferentiate functions with radicals.
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Evaluating Limits Algebraically, Part 1
Calculus Limits and Continuity
How to evaluate the limit of a function using continuity.
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Derivatives of Logarithmic Functions
Calculus The Derivative
How to infer the derivative of the natural log function using a calculator investigation.
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Continuity
Calculus Limits and Continuity
How to determine whether a function f(x) is continuous at a particular point x=a.
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Evaluating Limits Algebraically, Part 2
Calculus Limits and Continuity
How to evaluate the limit of a function at points where it is not continuous.
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Chain Rule: The General Logarithm Rule
Calculus Techniques of Differentiation
How to differentiate a composite function when the outside function is the natural logarithm.
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The Product Rule
Calculus Techniques of Differentiation
How to differentiate a product of two functions.
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Substitutions Involving e^x or ln(x)
Calculus Antiderivatives and Differential Equations
How to use the method of substitution when the antiderivatives involve e^x or ln[x].
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The Second Derivative Test for Relative Maximum and Minimum
Calculus Applications of the Derivative
How to show that polynomial functions are continuous functions.

Antidifferentiation
Calculus Antiderivatives and Differential Equations
How to find an antiderivative of a function.
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