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

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

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

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

\infty

Solution steps

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

x \to \infty lim (x - 1) = \infty

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

= \infty \cdot 1

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

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

\int \frac{1}{x x ^{2} + 5} d x

\frac{\partial}{\partial y} (\frac{x ^{2}}{2})

f (x) = x 3 - x

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