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}}) = \infty

= \frac{0}{\infty}

Apply Infinity Property:

\frac{0}{\infty} = 0

= 0

x \to - 3 lim (x^{2} + 5 x + 6)

x \to \infty lim (- x^{0})

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

x \to \infty lim (- 2 x + 5)

x \to 4 lim (lo g_{x} (x))

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