What is the limit as x approaches 0+of 3/(1+e^{1/x)} ?

The limit as x approaches 0+of 3/(1+e^{1/x)} is 0

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limit as x approaches 0+of 3/(1+e^{1/x)}

x \to 0 + lim (\frac{3}{1 + e ^{\frac{1}{x}}})

0

Solution steps

x \to 0 + lim (\frac{3}{1 + e ^{\frac{1}{x}}})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 3 \cdot x \to 0 + lim (\frac{1}{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

= 3 \cdot \frac{lim _{x \to 0 +} ( 1 )}{lim _{x \to 0 +} ( 1 + e ^{\frac{1}{x}} )}

x \to 0 + lim (1) = 1

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

= 3 \cdot \frac{1}{\infty}

Simplify

3 \cdot \frac{1}{\infty} : 0

= 0

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What is the limit as x approaches 0+of 3/(1+e^{1/x)} ?
The limit as x approaches 0+of 3/(1+e^{1/x)} is 0