Video shows how to use the definite integral of the velocity function of a particle to determine the distance traveled, average velocity and position of the particle at a given time. [14:37]

Video shows how to calculate the definite integral using a table of values and interprets what the definite integral represents in terms of the situation. Also shows how to use the definite integral to determine the value of a function...

Video demonstrates how to write the equation of a line tangent to a function at a given point. Also shows how to find the area between two curves using definite integrals. [8:13]

Video shows how to use limits to determine if a function is continuous at a given point. [4:23]

Video shows how to find the second derivative of a function and use it to determine if the answer found in the previous video which used the slope of the tangent line is an underestimate or overestimate. [8:18]

Video shows how to find the points of inflection of an unusal function by looking at a graph of the first derivative of the function. [4:24]

Video shows how to rewrite a differential equation as a derivative of a function and then use it to find the slope of the tangent line to a function at a given point. The tangent line is then used to estimate a future value of the...

Video shows how to determine the absolute maximum of a function over an interval by finding the value of the function at both ends of the interval and at any critical values. [13:15]

Video shows how to determine whether the speed of a particle is increasing or decreasing at a given time by using the velocity and acceleration functions and reasoning about the signs of the functions when evaluated at the given time....

Video shows how to find the particular solution to a separable differential equation. [9:15]

This video [5:15] shows how to write the derivative of a piecewise function as another piecewise function. Uses the derivative to find the value of x that gives a certain derivative value.

This video [4:48] shows how to determine the integral of an unusual function using geometry to find the area under the curve. Also shows how to find the derivative of a function which contains an integral by using the Fundamental Theorem...

Video shows how to use the disk method to write an integral representing the volume of the solid generated by rotating two intersecting functions around a line. [6:39]

Video shows how to calculate the average rate of change of a function over an interval and explains why it does not contradict the Mean Value Theorem. [5:46]

Video shows how to use a table of values to determine the approximate rate of change at a given time. Also explains what a definite integral means in terms of the situation and shows how to use a trapezoidal sum to estimate the integral....

Video shows how to find the integral of a piecewise function and use it to determine the average value of the function over a given interval. [7:29]