limits of integration 47 videos

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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Critical Points
Calculus Applications of the Derivative
How to find a twosided limit by investigating onesided limits.

The Derivative Function
Calculus The Derivative
How to define the derivative function f'(x).
derivative limits the derivative function 
The Method of Substitution
Calculus Antiderivatives and Differential Equations
How to evaluate an indefinite integral using the method of substitution.
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Intervals of Increase and Decrease
Calculus Applications of the Derivative
How to estimate a limit using a table of values.

Curve Sketching with Derivatives
Calculus Applications of the Derivative
How to evaluate the limit of a function using continuity.

Optimization Using the Closed Interval Method
Calculus Applications of the Derivative
How to evaluate the limit of a function at points where it is not continuous.

Simple Substitutions
Calculus Antiderivatives and Differential Equations
How to use the method of substitution to avoid common integration mistakes.
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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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The First Derivative Test for Relative Maximum and Minimum
Calculus Applications of the Derivative
How to use an algebraic approach to find onesided limits of a rational function, and how these limits can be used to find a vertical asymptote.

Relative Maxima and Minima
Calculus Applications of the Derivative
How to use onesided limits to find a vertical asymptote.

Instantaneous Velocity
Calculus The Derivative
How to estimate the instantaneous velocity of an object at t=2 by computing average velocities over shorter and shorter intervals of time.
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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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Optimization Using the First Derivative Test
Calculus Applications of the Derivative
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.