limit as x approaches 3+of (3x+4)/(x-3)

解

x \to 3 + lim (\frac{3 x + 4}{x - 3})

\infty

解答ステップ

x \to 3 + lim (\frac{3 x + 4}{x - 3})

\frac{3 x + 4}{x - 3} = (3 x + 4) \frac{1}{x - 3}

= x \to 3 + lim ((3 x + 4) \frac{1}{x - 3})

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 3 + lim (3 x + 4) \cdot x \to 3 + lim (\frac{1}{x - 3})

x \to 3 + lim (3 x + 4) = 13

x \to 3 + lim (\frac{1}{x - 3}) = \infty

= 13 \cdot \infty

無限大の特性を適用する:

c \cdot \infty = \infty

= \infty