limit as x approaches 0 of (sin(1/x))^x

解答

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

不存在

求解步骤

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

若

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

则极限不存在

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

不存在

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

= 不存在

x \to \infty lim (5 ln (x))

x \to 0 lim (1 - ln (x))

x \to 0 lim (\frac{tan ( k ) x}{x})

x \to 0 lim (\frac{5}{x} + \frac{5}{x ^{2} - x})

x \to 0 lim (\frac{x}{cot ( x )})