Hello,
This is my first post on this forum . I can't seem to decide what the limit of this relatively simple equation is:
lim x approaches minus infinity of [arctan(e^-x)]
Any help is greatly appreciated!
Darren
Let $\displaystyle t=-x$ so when $\displaystyle x\to-\infty,t\to\infty$ and then $\displaystyle \lim_{x\to -\infty}\arctan\left(e^{-x}\right)=\lim_{t\to\infty}\arctan\left(e^t\right)$, but $\displaystyle \arctan(x)$ and $\displaystyle e^x$ are continuos functions in $\displaystyle \mathbb{R}$ so we can rewrite the limit as $\displaystyle \arctan\left\{\exp\left(\lim_{t\to\infty}t\right)\ right\}=\arctan \left(\infty\right)=\frac{\pi}{2}$.