What is the limit as y approaches 0 of (sin(5y))/(7y) ?

The limit as y approaches 0 of (sin(5y))/(7y) is 5/7

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

limit as y approaches 0 of (sin(5y))/(7y)

y \to 0 lim (\frac{sin ( 5 y )}{7 y})

\frac{5}{7}

Decimal

0.71428 \dots

Solution steps

y \to 0 lim (\frac{sin ( 5 y )}{7 y})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{1}{7} \cdot y \to 0 lim (\frac{sin ( 5 y )}{y})

Apply L'Hopital's Rule

= \frac{1}{7} \cdot y \to 0 lim (\frac{cos ( 5 y ) \cdot 5}{1})

Plug in the value

y = 0

= \frac{1}{7} \cdot \frac{cos ( 5 \cdot 0 ) \cdot 5}{1}

Simplify

\frac{1}{7} \cdot \frac{cos ( 5 \cdot 0 ) \cdot 5}{1} : \frac{5}{7}

= \frac{5}{7}

What is the limit as y approaches 0 of (sin(5y))/(7y) ?
The limit as y approaches 0 of (sin(5y))/(7y) is 5/7