My first calculus problem

Calculus Level 2

Find the limit of x t a n ( π x ) x \cdot tan (\frac{π}{x}) as x approaches positive infinity. Give your answer up to two correct decimal places.


The answer is 3.14.

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1 solution

Manuel Kahayon
Jan 2, 2016

This can be compared to having the ratio of the perimeter of a polygon with infinitely many sides to its apothem divided by 2. Since a circle has infinite sides and has a circumference of 2 π r 2•π•r , we get pi!

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