(part 1)

It would be a waste to make a Riemann sum finder and not make more calculus-related “calculators.”

##### The Equation of a Tangent Line

We can find the equation of a function’s various tangent lines using the function’s derivative. This tool allows the user to manipulate the point where the tangent line hits any given function. Here is a video demonstration (link) and the source code (link). This is how the code was constructed:

- use Plot[] to draw the original function and the general equation for a tangent line (I used “n” as a placeholder for the x-value)
- use Epilog to draw the point where the tangent line meets the graph
- PlotLabel (in the graph) will equation of the tangent line, so use a combination of <> and ToString[]
- display the contact point’s coordinates next to the point using Text[] (tip: to get the position of the text, take the original point and offset it by a small amount)
- optional: change the colors to make it look cool

##### Revolution of Solids

The volume of a solid found by rotating a graph around the x-axis, y-axis, or another line can be found using integrals. This small widget displays the graph of the function, its revolution, and the area. The degree of revolution can be manipulated and a function can be entered. Here is a demonstration (link) and here is the source code (link). The following steps show how the code was created:

- plot a function using RevolutionPlot3D[]
- change the degree of revolution to 0 to “a” (the letter “a” will be manipulated as the degree of revolution)
- calculate the area of the solid for the PlotLabel (tip: the area should be pi times the integral of the function squared, from 0 to “a”)
- make sure the code works, then replace the function with the letter “f” (you should be able to enter the function, but make sure that there is an initial function)
- use Manipulate[] to change the values of “a” and “f” – make sure that “a” starts from a number close to but not equal to zero