1. ## Simple limit

$\lim_{x \rightarrow -1^+}\frac{\pi -arccosx}{x+1}$

2. ## Re: Simple limit

Looks to me like L'Hopital's rule will work here. The derivative of $\pi- arccos(x)$ is $-\sqrt{1- x^2}$ and, of course, the derivative of x+ 1 is 1.

3. ## Re: Simple limit

No, \displaystyle \begin{align*}\frac{d}{dx} \left[ \pi - \arccos{(x)} \right] = 0 - \left( -\frac{1}{\sqrt{1 - x^2}} \right) = \frac{1}{\sqrt{1 - x^2}} \end{align*}.

4. ## Re: Simple limit

Oops! Forgot the "1/" part!

5. ## Re: Simple limit

Thank you for helping!