What is the limit as x approaches 0+of 1/x*e^{1/x} ?

The limit as x approaches 0+of 1/x*e^{1/x} is infinity

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limit as x approaches 0+of 1/x*e^{1/x}

x \to 0 + lim (\frac{1}{x} \cdot e^{\frac{1}{x}})

\infty

Solution steps

x \to 0 + lim (\frac{1}{x} e^{\frac{1}{x}})

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 0 + lim (\frac{1}{x}) \cdot x \to 0 + lim (e^{\frac{1}{x}})

x \to 0 + lim (\frac{1}{x}) = \infty

x \to 0 + lim (e^{\frac{1}{x}}) = \infty

= \infty \cdot \infty

Apply Infinity Property:

\infty \infty = \infty

= \infty

f (x) = 3 cos (2 x)

y = \frac{8}{1 + x ^{4}}, y = 4 x^{2}

f (x) = \frac{1}{x - 4}

\int sec (d) x d x

\int (\frac{2}{x} + \frac{x}{2}) d x

What is the limit as x approaches 0+of 1/x*e^{1/x} ?
The limit as x approaches 0+of 1/x*e^{1/x} is infinity