The volume of a cone can be approximated by carving the cone into slices, and approximating each slice with a cylinder. To then set it up as a Riemann sum, it helps to orient the cone so that we can … Continue reading

# Tag Archives: Mathematica

The volume of a pyramid can be approximated by carving the pyramid into slices, and approximating each slice with a rectangular cuboid. To then set it up as a Riemann sum, it helps to orient the pyramid so that we … Continue reading

Without computing the integral, decide if is positive or negative, and explain your decision. Solution: We know that (in blue) is positive but decreasing. On the other hand, (in green) is positive on , and then repeats itself (but negative) … Continue reading

Some of the pages on this site use the Wolfram CDF Player, which you will need to install if you want to see everything on those pages. I like the player, except for one quality: it continues to run after … Continue reading

For practicing understanding the implications of lefthand vs. righthand (or lower bound vs. upper bound integrals), it's nice to be able to graph a function with a grid suited to the task. I plotted a portion of using Mathematica. f[x_] … Continue reading

There are lots of bells and whistles available in Mathematica, but sometimes I like something really plain. For example, I wanted my students to find slope analytically given two points. On graph paper with a full grid, they could count … Continue reading

If you are manually graphing slope fields, here are some scalable graphics: Slope field, grid Slope field, grid You can plot slope fields with a solution to the differential equation in Grapher (Mac only). If you haven't used Grapher, it … Continue reading

We make lots of graphs. Sometimes I embed the graphs in the handout. But other times, such as for creating graphs that will be cut out and attached to a group chart, a separate piece of graph paper is better. … Continue reading