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

解答

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

0

求解步骤

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

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

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

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

x \to 0 + lim (1) = 1

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

= 2 \cdot \frac{1}{- \infty}

化简

2 \cdot \frac{1}{- \infty} : 0

= 0

n \to \infty lim ((1 - \frac{3}{n})^{2 n})

x \to 4 lim (lo g_{5} (6 x + 1))

x \to 2 lim (12)

x \to \infty lim (\frac{3}{e ^{- x} + 2})

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