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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.

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

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 pass his position at 80 km/hr. One minute later, police officer Brady notices the same car pass his position 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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