What is the limit as x approaches 2 of (sin(8x))/x ?

The limit as x approaches 2 of (sin(8x))/x is 1/2 sin(16)

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limit as x approaches 2 of (sin(8x))/x

x \to 2 lim (\frac{sin ( 8 x )}{x})

\frac{1}{2} sin (16)

Decimal Notation

- 0.14395 \dots

Solution steps

x \to 2 lim (\frac{sin ( 8 x )}{x})

Plug in the value

x = 2

= \frac{sin ( 8 \cdot 2 )}{2}

Simplify

\frac{sin ( 8 \cdot 2 )}{2} : \frac{1}{2} sin (16)

= \frac{1}{2} sin (16)

x \to 0 lim (- x^{x})

x \to 0 + lim (- ln (x^{x}))

x \to 3 lim ((3 x - 10) + x)

x \to 0 lim (\frac{( 1 - e ^{x} )}{x})

x \to \frac{1}{3} lim ((2 - 3 x)^{2} + 1)

What is the limit as x approaches 2 of (sin(8x))/x ?
The limit as x approaches 2 of (sin(8x))/x is 1/2 sin(16)