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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.

# Calculus - Intermediate Warmup

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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