limit as x approaches 4+of (x+2)/(x-4)

解

x \to 4 + lim (\frac{x + 2}{x - 4})

\infty

解答ステップ

x \to 4 + lim (\frac{x + 2}{x - 4})

\frac{x + 2}{x - 4} = (x + 2) \frac{1}{x - 4}

= x \to 4 + lim ((x + 2) \frac{1}{x - 4})

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 4 + lim (x + 2) \cdot x \to 4 + lim (\frac{1}{x - 4})

x \to 4 + lim (x + 2) = 6

x \to 4 + lim (\frac{1}{x - 4}) = \infty

= 6 \cdot \infty

無限大の特性を適用する:

c \cdot \infty = \infty

= \infty