What is the limit as t approaches infinity of te^t ?

The limit as t approaches infinity of te^t is infinity

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limit as t approaches infinity of te^t

t \to \infty lim (t e^{t})

\infty

Solution steps

t \to \infty lim (t 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 (t) \cdot t \to \infty lim (e^{t})

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

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

= \infty \cdot \infty

Apply Infinity Property:

\infty \infty = \infty

= \infty

What is the limit as t approaches infinity of te^t ?
The limit as t approaches infinity of te^t is infinity