limit as x approaches 0+of 1/(1+1/x)

解答

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

0

求解步骤

x \to 0 + lim (\frac{1}{1 + \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

不定型除外

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

x \to 0 + lim (1) = 1

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

= \frac{1}{\infty}

运用无穷大属性:

\frac{c}{\infty} = 0

= 0