Question

How do you find the limit of `1/(x(1 + x²))` as x approaches `0^-`?

Answer 1

`lim_(x->0^-)1/(x(1+x^2))=-oo`

Explanation:

To find `lim_(x->0^-)1/(x(1+x^2))`, let us assume `x=0-h`,

then the limit begins `lim_(h->0)1/((-h)(1+(-h)^2))`

= `lim_(h->0)1/(-h(1+h^2)`

= `-lim_(h->0)1/(h(1+h^2)`

= `-oo`