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

解

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

- \infty

解答ステップ

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

簡素化

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

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

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

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

不定形式の場合を除く

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

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

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

= (- 1) \cdot \infty

無限大の特性を適用する:

- c \cdot \infty = - \infty

= - \infty