limit as x approaches 0+of 1/(x^2)-1/x

解答

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

\infty

求解步骤

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

化简

\frac{1}{x ^{2}} - \frac{1}{x} : \frac{1 - x}{x ^{2}}

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

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

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

x \to 0 + lim (1 - x) = 1

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

= 1 \cdot \infty

运用无穷大属性:

c \cdot \infty = \infty

= \infty

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d er i v a t i v e f (x) = \frac{x ^{2}}{x + 7}

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