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 Notation

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)

d y = (4 x - 6) d x

\frac{d y}{d x} + \frac{1}{3} y = \frac{1}{3} (1 - 2 x) y^{4}

x^{4} \frac{d y}{d x} - 2 x^{3} y = 4 x^{6} - 3 x^{2}

\int \frac{x ^{2} - 196}{x} d x

\int \frac{1}{x ^{2} - a ^{2}} d x

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)