1. ## evaluating limits

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.

ArTiCk

2. Originally Posted by ArTiCK
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.

ArTiCk
The limit is of the form
$\frac{\pi}{0}$

Any limit of the form (something other than 0)/0 does not exist as the operation is undefined. Only when you have 0/0 is it possible to have a solution (but it won't always.)

-Dan

3. Originally Posted by ArTiCK
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.

ArTiCk
Originally Posted by topsquark
The limit is of the form
$\frac{\pi}{0}$

Any limit of the form (something other than 0)/0 does not exist as the operation is undefined. Only when you have 0/0 is it possible to have a solution (but it won't always.)

-Dan
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:

$\lim_{x \rightarrow -3^+} \frac{\pi}{(x+3)^3} = + \infty$.

$\lim_{x \rightarrow -3^-} \frac{\pi}{(x+3)^3} = - \infty$.

Technically $\lim_{x \rightarrow -3} \frac{\pi}{(x+3)^{\color{red}2}}$ does exist: $~ \lim_{x \rightarrow -3} \frac{\pi}{(x+3)^2} = + \infty$ ......

Where's referee TPH ....?