What is the limit as x approaches 0-of 1/(2+e^{1/x)} ?

The limit as x approaches 0-of 1/(2+e^{1/x)} is 1/2

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limit as x approaches 0-of 1/(2+e^{1/x)}

x \to 0 - lim (\frac{1}{2 + e ^{\frac{1}{x}}})

\frac{1}{2}

Decimal Notation

0.5

Solution steps

x \to 0 - lim (\frac{1}{2 + 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 -} ( 1 )}{lim _{x \to 0 -} ( 2 + e ^{\frac{1}{x}} )}

x \to 0 - lim (1) = 1

x \to 0 - lim (2 + e^{\frac{1}{x}}) = 2

= \frac{1}{2}

\int_{0}^{2} 2 x - x^{2} d x

9 x, x^{2} - 10

\frac{\partial}{\partial x} (yz + x ln (y) - z^{2})

\frac{3}{x + 2}

n = 1 \sum \infty \frac{1}{( 2 n - 1 ) ^{4}}

What is the limit as x approaches 0-of 1/(2+e^{1/x)} ?
The limit as x approaches 0-of 1/(2+e^{1/x)} is 1/2