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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 Warmups: Level 1 Challenges

Every time Pinocchio tells a lie, his nose grows one inch longer.

When he left this morning, Pinocchio's nose was only 3 inches long. However, when he arrived home for dinner, his creator Geppetto noticed that his nose was now 9 inches long.

How many lies did Pinocchio tell while he was away?

The above shows the profile of the Hoosac Mountain. Between which points is the slope the steepest?

What is the slope of the line tangent to the parabola shown in the figure above?

Evaluate

$\displaystyle \lim_{x \to \infty} \frac {1}{x}$

The Eiffel Tower was the tallest structure in the world until 1930. If the first three images above were taken on March 1888, July 1888, and November 1888, which of the following dates is the most reasonable for the final picture of the completed tower?

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