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人気のある微分積分 >

limit as x approaches-3+of (-2x^2)/((x-1)(x+3))

解

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

解

\infty

解答ステップ

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

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

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

以下の代数プロパティを適用する

: a + b = a (1 + \frac{b}{a})

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

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

簡素化

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

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

右側から

- 3

に近づく

x

の場合は,

x > - 3 \Rightarrow (- \frac{1}{x} + 1) (\frac{3}{x} + 1) < 0

分母は左から0に近づく負の数量

= - 2 (- \infty)

無限大の特性を適用する:

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

= \infty

グラフ

人気の例

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