Question

How do you determine the limit of `[1/(x-2) + 1/(x+2)]` as x approaches 2+?

Answer 1

The Limit in question does not exist.

Explanation:

To find `lim_(xrarr2+){1/(x-2)+1/(x+2)}`, we note that,

As `xrarr2+, x>2, (x-2)>0, i.e., (x-2)rarr0+`

`rArr1/(x-2)rarr oo`

Thus, despite `lim_(xrarr2+)1/(x+2)=1/4`, we find that,

`lim_(xrarr2+){1/(x-2)+1/(x+2)}` does not exist.