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Problem 26 Easy Difficulty

Evaluate the limit, if it exists.

$ \displaystyle \lim_{t \to 0}\left( \frac{1}{t} - \frac{1}{t^2 + t} \right) $

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1

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Video Transcript

to find the limit of one over t minus one over t squared plus T as T approaches zero. We first write this into to limit as T approaches zero of one over t minus one over T. Time. Sleepless one. And then from here we can combine the two fractions and we have the limit as T approaches zero of we have a common denominator of tee times deepest one, and the first term of the numerator would be T plus one this minus one. And then simplifying this. We have limit S. T approaches zero of T over tee times T plus one. And here we can cancel out the tea and we have the limit as T approaches zero of one over T plus one. And so evaluating this limit we have 1/0 plus one or that's 1/1 equal to one. Therefore this is the limit value.