limit as t approaches infinity of te^t

解

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

\infty

解答ステップ

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)

不定形式の場合を除く

= 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

無限大の特性を適用する:

\infty \infty = \infty

= \infty