What is the limit as x approaches infinity of x^{2e^{-x}} ?

The limit as x approaches infinity of x^{2e^{-x}} is 1

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limit as x approaches infinity of x^{2e^{-x}}

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

1

Solution steps

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

Apply exponent rules

= x \to \infty lim (e^{2 e^{- x} l n (x)})

Apply the Limit Chain Rule:

1

= 1

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

x \to 0 + lim (4 x ln (x))

x \to - \infty lim (\frac{6}{x})

x \to 0 lim (3 x cot (2 x))

x \to 0 - lim (\frac{2}{x ^{3}})

What is the limit as x approaches infinity of x^{2e^{-x}} ?
The limit as x approaches infinity of x^{2e^{-x}} is 1