Having side-by-side comparisons can be valuable experience as similarities (and differences) are more readily apparent; students can gain a deeper understanding of the nuances from one to the next. For example, its worth noting that the rate of change of a circle’s area with respect to its radius is equal to that circle’s circumference; a similar relationship exists between the volume and surface area of a sphere.

Investing some thought into these and other subtleties can go a long way towards increasing one’s intuitive feel for, and enjoyment of this discipline.

Another comparison worth checking out is quadratic vs exponential growth.

Thanks for reading.

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