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

解答

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

发散

求解步骤

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

若

x \to a^{-} lim f (x) \neq = x \to a^{+} lim f (x)

则极限不存在

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

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

= 发散

x \to 0 lim (e^{x} cos (x))

x \to 2 lim (5 x + 2)

x \to - \infty lim (- 2 x)

x \to 0 lim (\frac{e ^{a x} - e ^{b x}}{sin ( a x ) - sin ( b x )})

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