Expert answers to "Find the limits: limt→1t2+t−2t2−1"

Amari Flowers

Answered question

2021-02-20

Find the limits:

lim_{t \to 1} \frac{t^{2} + t - 2}{t^{2} - 1}

Alara Mccarthy

Skilled2021-02-21Added 85 answers

Given that:

lim_{t \to 1} \frac{t^{2} + t - 2}{t^{2} - 1}

Solve:
We have,

lim_{t \to 1} \frac{t^{2} + t - 2}{t^{2} - 1}

Since the limit is an INDETERMINATE form of type

\frac{0}{0}

Therefore, Applying LHopitals Rule we obtain,

lim_{t \to 1} \frac{t^{2} + t - 2}{t^{2} - 1} = lim_{t \to 1} \frac{\frac{d}{d t} (t^{2} + t - 2)}{\frac{d}{d t} (t^{2} - 1)}

= lim_{t \to 1} \frac{2 t + 1}{2 t}

= \frac{2 (1) + 1}{2 (1)}

= \frac{2 + 1}{2}

\frac{3}{2}

Jeffrey Jordon

Expert2022-04-01Added 2605 answers

Answer is given below (on video)

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