Question

How do you find the limit of `1/x [(1/(2+x) -1/2)]` as x approaches 0?

Answer 1

`= - 1/4`

Explanation:

`lim_{x to 0} 1/x (1/(2+x) -1/2)`

`lim_{x to 0} 1/x ((2 - 2 - x)/(2(2+x)) )`

`lim_{x to 0} 1/x (( - x)/(2(2+x)) )`

`lim_{x to 0} ((-1)/(2(2+x)) )`

`= - 1/4`