continuity and limits 38 videos

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 Second Derivative Test for Relative Maximum and Minimum
Calculus Applications of the Derivative
How to show that polynomial functions are continuous functions.

The Fundamental Theorem of Calculus
Calculus The Definite Integral
How to use the fundamental theorem of calculus to evaluate a definite integral.
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Intervals of Increase and Decrease
Calculus Applications of the Derivative
How to estimate a limit using a table of values.

Computing Definite Integrals using Substitution
Calculus The Definite Integral
How to evaluate definite integrals using the method of substitution.
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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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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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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.

Instantaneous Rate of Change
Calculus The Derivative
How to estimate the instantaneous rate liquid is pouring out of a container at t=4 by computing average rates of change over shorter and shorter intervals of time.
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The Definition of the Derivative
Calculus The Derivative
How to define the derivative of a function at a point x=a.
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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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Approximating Area Using Rectangles
Calculus The Definite Integral
How to approximate the area under a curve using rectangles.
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