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人気のある微分積分 >

limit as x approaches infinity of 2x-sqrt(4x^2-2x)

解

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

解

\frac{1}{2}

+1

十進法表記

0.5

解答ステップ

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

2 x - 4 x^{2} - 2 x

の共役で乗じる

\frac{2 x}{2 x + 4 x ^{2} - 2 x}

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

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

= 2 \cdot x \to \infty lim (\frac{x}{2 x + 4 x ^{2} - 2 x})

最高の分母べき乗で割る:

\frac{1}{2 + 4 - \frac{2}{x}}

= 2 \cdot x \to \infty lim \frac{1}{2 + 4 - \frac{2}{x}}

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

不定形式の場合を除く

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

x \to \infty lim (1) = 1

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

= 2 \cdot \frac{1}{4}

簡素化

2 \cdot \frac{1}{4} : \frac{1}{2}

= \frac{1}{2}

グラフ

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