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 0 of x/(tan(4x))

解

x \to 0 lim (\frac{x}{tan ( 4 x )})

解

\frac{1}{4}

+1

十進法表記

0.25

解答ステップ

x \to 0 lim (\frac{x}{tan ( 4 x )})

サイン, コサインで表わす

= x \to 0 lim (\frac{x cos ( 4 x )}{sin ( 4 x )})

基本的な三角関数の公式を使用する:

\frac{cos ( x )}{sin ( x )} = cot (x)

= x \to 0 lim (x cot (4 x))

ロピタル向けに書き換える

= x \to 0 lim (\frac{x}{\frac{1}{c o t ( 4 x )}})

ロピタルの定理を適用する

= x \to 0 lim (\frac{1}{sec ^{2} ( 4 x ) \cdot 4})

値を挿入する

x = 0

= \frac{1}{sec ^{2} ( 4 \cdot 0 ) \cdot 4}

sec^{2} (4 \cdot 0) \cdot 4 = 4

= \frac{1}{4}

グラフ

人気の例

limit as x approaches 0 of (2x^2)/(3-3cos(x))

x \to 0 lim (\frac{2 x ^{2}}{3 - 3 cos ( x )})

limit as x approaches 0 of (x+e^x)^{2/x}

x \to 0 lim ((x + e^{x})^{\frac{2}{x}})

limit as x approaches 4 of (x-4)/(x+1)

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

limit as x approaches 1 of x^{x/(1-x)}

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

limit as x approaches 2 of (2x-5)/(x-2)

x \to 2 lim (\frac{2 x - 5}{x - 2})