limit as x approaches 2+of (1-x)/(x-2)

解答

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

- \infty

求解步骤

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

\frac{1 - x}{x - 2} = (1 - x) \frac{1}{x - 2}

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

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

不定型除外

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

x \to 2 + lim (1 - x) = - 1

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

= (- 1) \cdot \infty

运用无穷大属性:

- c \cdot \infty = - \infty

= - \infty

\int_{0}^{2} \frac{1}{4 - x ^{2}} d x

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a re a 3 x^{4} - 3 x^{2}, 6 x^{2}