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

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

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limit as t approaches-infinity of ((-2t-2))/(e^t)

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

\infty

Solution steps

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

\frac{- 2 t - 2}{e ^{t}} = (- 2 t - 2) \frac{1}{e ^{t}}

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

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

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

t \to - \infty lim (- 2 t - 2) = \infty

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

= \infty \cdot \infty

Apply Infinity Property:

\infty \infty = \infty

= \infty

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