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人気のある微分積分 >

limit as x approaches-2-of (x^2)/(3x+6)

解

x \to - 2 - lim (\frac{x ^{2}}{3 x + 6})

解

- \infty

解答ステップ

x \to - 2 - lim (\frac{x ^{2}}{3 x + 6})

3 x

を

3 x + 6 : 3 x (1 + \frac{6}{3 x})

からくくり出す

= x \to - 2 - lim (\frac{x ^{2}}{3 x ( 1 + \frac{6}{3 x} )})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{1}{3} \cdot x \to - 2 - lim (\frac{x ^{2}}{x ( 1 + \frac{6}{3 x} )})

簡素化

\frac{x ^{2}}{x ( 1 + \frac{6}{3 x} )} : \frac{x ^{2}}{x + 2}

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

\frac{x ^{2}}{x + 2} = x^{2} \frac{1}{x + 2}

= \frac{1}{3} \cdot x \to - 2 - lim (x^{2} \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

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

x \to - 2 - lim (x^{2}) = 4

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

= \frac{1}{3} \cdot 4 (- \infty)

無限大の特性を適用する:

c \cdot (- \infty) = - \infty

= - \infty

グラフ

人気の例

limit as x approaches 4 of 5x+2

x \to 4 lim (5 x + 2)

limit as x approaches-3 of 2x

x \to - 3 lim (2 x)

limit as x approaches-pi/2+of-3x-pi/2

x \to - \frac{π}{2} + lim (- 3 x - \frac{π}{2})

limit as x approaches 0+of 2x*ln(x)

x \to 0 + lim (2 x \cdot ln (x))

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

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