Hi all,
I need some help evaluating the following limit:
lim x-->-3 pi/(x+3)^3
I believe that the limit does not exist but i don't know how to explain it.
Thanks in advance,
ArTiCk
Topsquark, this is a very rare (the only, so far?) occassion when I will disagree with you .....
The limit does not exist because the left hand limit is not equal to the right hand limit:
$\displaystyle \lim_{x \rightarrow -3^+} \frac{\pi}{(x+3)^3} = + \infty$.
$\displaystyle \lim_{x \rightarrow -3^-} \frac{\pi}{(x+3)^3} = - \infty$.
Technically $\displaystyle \lim_{x \rightarrow -3} \frac{\pi}{(x+3)^{\color{red}2}}$ does exist: $\displaystyle ~ \lim_{x \rightarrow -3} \frac{\pi}{(x+3)^2} = + \infty$ ......
Where's referee TPH ....?