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skomminbv

Answered question

2021-12-01

How do you find the limit as x approaches infinity of

y = \arctan (e^{x})

tnie54

Beginner2021-12-02Added 18 answers

lim_{x \Rightarrow + \infty} e^{x} = + \infty

and

lim_{x \Rightarrow + \infty} \arctan (x) = \frac{π}{2}

.
Thus, if

x \Rightarrow \infty

e^{x} \Rightarrow \infty

so that, letting

t = e^{x}

, you have:

lim_{x \Rightarrow + \infty} \arctan (e^{x}) = lim_{t \Rightarrow + \infty} \arctan (t) = \frac{π}{2}

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