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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. See more

Calculus - Basic

\[\Large \frac{1}{2^0}, \frac{1}{2^1}, \frac{1}{2^2}, \frac{1}{2^3}, \frac{1}{2^4}, \ldots \]

True or False?

The sequence above approaches 0.

True or False?

The slope of the red line is 0.

Police officers Alfred and Brady are stationed two kilometers apart on a road where the speed limit is 100 km/hr.

Alfred notices a car traveling at 80 km/hr. One minute later, police officer Brady notices the same car traveling at 80 km/hr.

Was this car driving over the speed limit as it drove along the road?

\[ \lim_{x \rightarrow 1 } \frac{ x^2 - 1 } { x - 1 } \]

Which of the following statement is true of the above limit?

True or False?

The following infinite sum converges:

\[ \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \ldots \]

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