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# Calculus Warmups

The concepts of limits, infinitesimal partitions, and continuously changing quantities paved the way to Calculus, the universal tool for modeling continuous systems from Physics to Economics.

True or False?

If we differentiate the volume of a sphere with respect to the radius, we will obtain the surface area.

True or False?

The constant \( e \) is rational.

True or False?

\(i^ i \) is **not** a real number.

True or False?

\[ \frac{1}{ 1^2 } + \frac{1}{2^2 } + \frac{ 1 } { 3^2 } + \frac{1}{4^2 } + \ldots = \frac{ \pi ^2 } { 6 } \]

True or False?

There is a volume of revolution which has infinite volume but finite surface area.

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