# What is the limit of Tan(x) as x approaches infinity?

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Alan P. Share
Feb 15, 2016

$\tan \left(x\right)$ does not converge as $x \rightarrow \infty$

#### Explanation:

Here is the graph for $\tan \left(x\right)$:
graph{tan(x) [-10, 10, -5, 5]}
No matter how large a value you choose for $x$ the range $\tan \left(x - \pi\right)$ to $\tan \left(x + \pi\right)$ will cover all values $\left(- \infty , + \infty\right)$

${\lim}_{x \rightarrow \infty} \tan \left(x\right)$ does not exist.

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