What is the limit as x approaches infinity of x(e^{1/x-1}) ?

The limit as x approaches infinity of x(e^{1/x-1}) is infinity

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limit as x approaches infinity of x(e^{1/x-1})

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

\infty

Solution steps

x \to \infty lim (x e^{\frac{1}{x} - 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

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

x \to \infty lim (x) = \infty

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

= \infty \cdot \frac{1}{e}

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

x \to 1 lim (sin (x - 1))

x \to 4 lim (3 x + 2)

x \to 0 lim ((x)^{(x^{2})})

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

x \to 2 + lim (\frac{1}{x - 2})

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