rational 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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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 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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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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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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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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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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Limits and End Behavior
Calculus Limits and Continuity
How to evaluate the limit of a function as x goes to infinity (or minus infinity), and how to determine the horizontal asymptote of its graph.
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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.