What is the limit as x approaches 0 of (sin(5x))/(tan(x)) ?

The limit as x approaches 0 of (sin(5x))/(tan(x)) is 5

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(5x))/(tan(x))

x \to 0 lim (\frac{sin ( 5 x )}{tan ( x )})

5

Solution steps

x \to 0 lim (\frac{sin ( 5 x )}{tan ( x )})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{cos ( 5 x ) \cdot 5}{sec ^{2} ( x )})

Plug in the value

x = 0

= \frac{cos ( 5 \cdot 0 ) \cdot 5}{sec ^{2} ( 0 )}

Simplify

\frac{cos ( 5 \cdot 0 ) \cdot 5}{sec ^{2} ( 0 )} : 5

= 5

What is the limit as x approaches 0 of (sin(5x))/(tan(x)) ?
The limit as x approaches 0 of (sin(5x))/(tan(x)) is 5