# Thread: Limit with indeterminate form

1. ## Limit with indeterminate form

$\lim \limits_{t \to 0}(\frac{1}{t}-\frac{1}{t^2+t})$

I wasn't sure what to do with this problem on a test and got it wrong. Substituting 0 directly into the problem didn't seem to help me as it became an indeterminate form. I know the answer is 1 now, but I still can't reverse evaluate the limit. I factored ${t^2+t}$, but I don't know really where to go from there.

2. ## Re: Limit with indeterminate form

Originally Posted by AZach
$\lim \limits_{t \to 0}(\frac{1}{t}-\frac{1}{t^2+t})$

I wasn't sure what to do with this problem on a test and got it wrong. Substituting 0 directly into the problem didn't seem to help me as it became an indeterminate form. I know the answer is 1 now, but I still can't reverse evaluate the limit. I factored ${t^2+t}$, but I don't know really where to go from there.
\displaystyle \begin{align*} \lim_{t \to 0} \left( \frac{1}{t} - \frac{1}{t^2 + t} \right) &= \lim_{t \to 0} \left[ \frac{t + 1}{t(t + 1)} - \frac{1}{t(t + 1)} \right] \\ &= \lim_{t \to 0} \left[ \frac{t}{t(t + 1)} \right] \\ &= \lim_{t \to 0}\left( \frac{1}{t + 1} \right) \\ &= \frac{1}{0 + 1} \\ &= 1 \end{align*}