What is the limit as x approaches 3 of (sin(5x))/x ?

The limit as x approaches 3 of (sin(5x))/x is 1/3 sin(15)

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limit as x approaches 3 of (sin(5x))/x

x \to 3 lim (\frac{sin ( 5 x )}{x})

\frac{1}{3} sin (15)

Decimal

0.21676 \dots

Solution steps

x \to 3 lim (\frac{sin ( 5 x )}{x})

Plug in the value

x = 3

= \frac{sin ( 5 \cdot 3 )}{3}

Simplify

\frac{sin ( 5 \cdot 3 )}{3} : \frac{1}{3} sin (15)

= \frac{1}{3} sin (15)

What is the limit as x approaches 3 of (sin(5x))/x ?
The limit as x approaches 3 of (sin(5x))/x is 1/3 sin(15)