What is the limit as x approaches 2 of (sin(2x))/x ?

The limit as x approaches 2 of (sin(2x))/x is 1/2 sin(4)

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limit as x approaches 2 of (sin(2x))/x

x \to 2 lim (\frac{sin ( 2 x )}{x})

\frac{1}{2} sin (4)

Decimal

- 0.37840 \dots

Solution steps

x \to 2 lim (\frac{sin ( 2 x )}{x})

Plug in the value

x = 2

= \frac{sin ( 2 \cdot 2 )}{2}

Simplify

\frac{sin ( 2 \cdot 2 )}{2} : \frac{1}{2} sin (4)

= \frac{1}{2} sin (4)

What is the limit as x approaches 2 of (sin(2x))/x ?
The limit as x approaches 2 of (sin(2x))/x is 1/2 sin(4)