Question

What is `lim_(trarr0) (1/t -1/(t^2+t))`?

Answer 1

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

Explanation:

`1/t - 1/(t^2+t) = (t+1)/(t^2+t) - 1/(t^2+t) = t/(t(t+1)) = 1/(t+1)`

with exclusion `t != 0`

So

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

Answer 2

It is

`lim_(trarr0) (1/t -1/(t^2+t))=lim_(trarr0) (t^2+t-t)/(t^2(t+1))=lim_(trarr0) 1/(t+1)=1`