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 (1-cos(3x))/(1-cos(7x))

解

x \to 0 lim (\frac{1 - cos ( 3 x )}{1 - cos ( 7 x )})

解

\frac{9}{49}

+1

十進法表記

0.18367 \dots

解答ステップ

x \to 0 lim (\frac{1 - cos ( 3 x )}{1 - cos ( 7 x )})

ロピタルの定理を適用する

= x \to 0 lim (\frac{3 sin ( 3 x )}{7 sin ( 7 x )})

ロピタルの定理を適用する

= x \to 0 lim (\frac{9 cos ( 3 x )}{49 cos ( 7 x )})

値を挿入する

x = 0

= \frac{9 cos ( 3 \cdot 0 )}{49 cos ( 7 \cdot 0 )}

簡素化

\frac{9 cos ( 3 \cdot 0 )}{49 cos ( 7 \cdot 0 )} : \frac{9}{49}

= \frac{9}{49}

グラフ

人気の例

limit as x approaches 3+of x^2-9

x \to 3 + lim (x^{2} - 9)

limit as (x,y) approaches (0,2) of x^3y

(x, y) \to (0, 2) lim (x^{3} y)

derivative of 40x

\frac{d}{d x} (40 x)

limit as x approaches 2-of e^{3/(2-x)}

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

derivative of y^2=16x

\frac{d}{d x} (y^{2}) = 16 x