San Antonio College Library

The Fundamental Theorem of Calculus is the theorem that relates the derivative to the integral.

This video shows how to find the equilibrium quantity, equilibrium price, and consumer and producer surplus of a system, given equations for supply and demand.

In this video, learn about rectilinear motion which is also horizontal motion.

Given two equations, one for x and one for y, both in terms of a third parameter variable t, eliminating the parameter is as simple as solving one of the equations for t and making a substitution into the other equation. This will leave you with one equation instead of two, which will be in terms of x and y only, the parameter variable having been eliminated.

To find the work required to pump water out of a tank, you need to model the work required to pump out a small slice of the water, and then transform that into integral notation in order to find the work required to pump out all the water.

This is an example of how to find the present value of a continuous income stream (regular deposits) after t years, assuming an interest rate r and that interest is compounded continuously.

If the work being done isn't consistent, but if instead the force varies, then you can find work done by the variable force using the method from this video.

To convert a polar equation (an equation in terms of polar coordinates (r, theta)), just use the conversion formulas in this video to replace all of the r and theta variables with x and y variables.

To convert a rectangular equation (an equation in terms of rectangular, or cartesian coordinates (x, y)), just use the conversion formulas in this video to replace all of the x and y variables with r and theta variables.

To use substitution to solve a limit problem, just plug the number you're approaching into the function. If you get a real-number answer, then the substitution worked. If not, you'll need to use a different technique to solve for the limit.