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

解

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

\infty

解答ステップ

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

簡素化

ln (x) + \frac{1}{x ^{2}} : \frac{x ^{2} ln ( x ) + 1}{x ^{2}}

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

\frac{x ^{2} ln ( x ) + 1}{x ^{2}} = (x^{2} ln (x) + 1) \frac{1}{x ^{2}}

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

x \to 0 + lim (x^{2} ln (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