What is the limit as x approaches 0 of (sin(7x))/(tan(11x)) ?

The limit as x approaches 0 of (sin(7x))/(tan(11x)) is 7/11

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

limit as x approaches 0 of (sin(7x))/(tan(11x))

x \to 0 lim (\frac{sin ( 7 x )}{tan ( 11 x )})

\frac{7}{11}

Decimal

0.63636 \dots

Solution steps

x \to 0 lim (\frac{sin ( 7 x )}{tan ( 11 x )})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{cos ( 7 x ) \cdot 7}{sec ^{2} ( 11 x ) \cdot 11})

Plug in the value

x = 0

= \frac{cos ( 7 \cdot 0 ) \cdot 7}{sec ^{2} ( 11 \cdot 0 ) \cdot 11}

Simplify

\frac{cos ( 7 \cdot 0 ) \cdot 7}{sec ^{2} ( 11 \cdot 0 ) \cdot 11} : \frac{7}{11}

= \frac{7}{11}

What is the limit as x approaches 0 of (sin(7x))/(tan(11x)) ?
The limit as x approaches 0 of (sin(7x))/(tan(11x)) is 7/11