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

解

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

\infty

解答ステップ

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

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

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

x \to 2 + lim (x^{2} - 1) = 3

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

= 3 \cdot \infty

無限大の特性を適用する:

c \cdot \infty = \infty

= \infty