ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある微分積分 >

limit as x approaches infinity of sqrt((12x^3-4x+1)/(1+3x+2x^3))

解

x \to \infty lim (\frac{12 x ^{3} - 4 x + 1}{1 + 3 x + 2 x ^{3}})

解

6

+1

十進法表記

2.44948 \dots

解答ステップ

x \to \infty lim (\frac{12 x ^{3} - 4 x + 1}{1 + 3 x + 2 x ^{3}})

最高の分母べき乗で割る:

\frac{12 - \frac{4}{x ^{2}} + \frac{1}{x ^{3}}}{\frac{1}{x ^{3}} + \frac{3}{x ^{2}} + 2}

= x \to \infty lim (\frac{12 - \frac{4}{x ^{2}} + \frac{1}{x ^{3}}}{\frac{1}{x ^{3}} + \frac{3}{x ^{2}} + 2})

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

不定形式の場合を除く

= x \to \infty lim (\frac{12 - \frac{4}{x ^{2}} + \frac{1}{x ^{3}}}{\frac{1}{x ^{3}} + \frac{3}{x ^{2}} + 2})

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

= \frac{lim _{x \to \infty} ( 12 - \frac{4}{x ^{2}} + \frac{1}{x ^{3}} )}{lim _{x \to \infty} ( \frac{1}{x ^{3}} + \frac{3}{x ^{2}} + 2 )}

x \to \infty lim (12 - \frac{4}{x ^{2}} + \frac{1}{x ^{3}}) = 12

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

= \frac{12}{2}

簡素化

= 6

グラフ

人気の例

integral from-3 to 3 of |x|-(x^2-6)

\int_{- 3}^{3} ∣ x ∣ - (x^{2} - 6) d x

integral from 5 to 6 of x/(x-5)

\int_{5}^{6} \frac{x}{x - 5} d x

integral of (x^2)/(x+5)

\int \frac{x ^{2}}{x + 5} d x

integral of (x-3)/(x^3+3x^2+2x)

\int \frac{x - 3}{x ^{3} + 3 x ^{2} + 2 x} d x

integral of e^{-(2r)/a}

\int e^{- \frac{2 r}{a}} d r