limit as x approaches 0 of (x-sin(x))/x

解答

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

0

求解步骤

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

除以分母的最高次幂:

1 - \frac{sin ( x )}{x}

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

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

不定型除外

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

x \to 0 lim (1) = 1

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

= 1 - 1

化简

= 0

\frac{\partial}{\partial y} (y sin (y))

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\int_{0}^{1} 6 e^{- 4 x} d x