What is the limit as t approaches 1-of (2t)/(t^2-1) ?

The limit as t approaches 1-of (2t)/(t^2-1) is -infinity

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limit as t approaches 1-of (2t)/(t^2-1)

t \to 1 - lim (\frac{2 t}{t ^{2} - 1})

- \infty

Solution steps

t \to 1 - lim (\frac{2 t}{t ^{2} - 1})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 2 \cdot t \to 1 - lim (\frac{t}{t ^{2} - 1})

\frac{t}{t ^{2} - 1} = t \frac{1}{t ^{2} - 1}

= 2 \cdot t \to 1 - lim (t \frac{1}{t ^{2} - 1})

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

= 2 \cdot t \to 1 - lim (t) \cdot t \to 1 - lim (\frac{1}{t ^{2} - 1})

t \to 1 - lim (t) = 1

t \to 1 - lim (\frac{1}{t ^{2} - 1}) = - \infty

= 2 \cdot 1 \cdot (- \infty)

Apply Infinity Property:

c \cdot (- \infty) = - \infty

= - \infty

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What is the limit as t approaches 1-of (2t)/(t^2-1) ?
The limit as t approaches 1-of (2t)/(t^2-1) is -infinity