What is the limit as x approaches 1 of ((sin(pix)))/(sin(3pix)) ?

The limit as x approaches 1 of ((sin(pix)))/(sin(3pix)) is 1/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

limit as x approaches 1 of ((sin(pix)))/(sin(3pix))

x \to 1 lim (\frac{( sin ( π x ) )}{sin ( 3 π x )})

\frac{1}{3}

Decimal

0.33333 \dots

Solution steps

x \to 1 lim (\frac{sin ( π x )}{sin ( 3 π x )})

Apply L'Hopital's Rule

= x \to 1 lim (\frac{cos ( π x ) π}{cos ( 3 π x ) \cdot 3 π})

Plug in the value

x = 1

= \frac{cos ( π 1 ) π}{cos ( 3 π 1 ) \cdot 3 π}

Simplify

\frac{cos ( π 1 ) π}{cos ( 3 π 1 ) \cdot 3 π} : \frac{1}{3}

= \frac{1}{3}

What is the limit as x approaches 1 of ((sin(pix)))/(sin(3pix)) ?
The limit as x approaches 1 of ((sin(pix)))/(sin(3pix)) is 1/3