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

The limit as x approaches 0-of x/(1+e^{1/x)} is 0

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limit as x approaches 0-of x/(1+e^{1/x)}

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

0

Solution steps

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

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

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

x \to 0 - lim (x) = 0

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

= \frac{0}{1}

Apply rule

\frac{0}{a} = 0, a \neq = 0

= 0

What is the limit as x approaches 0-of x/(1+e^{1/x)} ?
The limit as x approaches 0-of x/(1+e^{1/x)} is 0