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lim t->inf (2t2 + 3t + 1) / (t2 - 1)

August 20, 2026Mathematics

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Answer

2

4 steps

Divide every term in the numerator and the denominator by the highest power of $t$ in the denominator, which is $t^2$ .
$\lim_{t \to \infty} \frac{\frac{2t^2}{t^2} + \frac{3t}{t^2} + \frac{1}{t^2}}{\frac{t^2}{t^2} - \frac{1}{t^2}}$
Simplify the terms.
$\lim_{t \to \infty} \frac{2 + \frac{3}{t} + \frac{1}{t^2}}{1 - \frac{1}{t^2}}$
Apply the limit as $t \to \infty$ .
Recall that $\lim_{t \to \infty} \frac{c}{t^n} = 0$ for any constant $c$ and $n > 0$ .
$\frac{2 + 0 + 0}{1 - 0}$
Calculate the final value.
$\frac{2}{1} = 2$
The limit is:
$2$

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