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

解

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

0

解答ステップ

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

不定形式の場合を除く

= \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}}) = \infty

= \frac{1}{\infty}

無限大の特性を適用する:

\frac{c}{\infty} = 0

= 0