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

解答

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

0

求解步骤

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

化简

e^{- \frac{1}{x}} : \frac{1}{e ^{\frac{1}{x}}}

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

使用分式法则:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

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

x \to 0 + lim (1) = 1

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

= \frac{1}{\infty}

运用无穷大属性:

\frac{c}{\infty} = 0

= 0

x \to - 2 lim (∣ x ∣)

t an g e n t f (x) = \frac{7}{1 - x}, at x = - 3

d er i v a t i v e 8 z^{2} e^{z}

\frac{d ^{2}}{d x ^{2}} (\frac{x ^{2} + 1}{x ^{2} - 4})

\int \frac{7}{x - 2} d x