What is the limit as x approaches 0 of ([sin(8x)])/x ?

The limit as x approaches 0 of ([sin(8x)])/x is 8

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limit as x approaches 0 of ([sin(8x)])/x

x \to 0 lim (\frac{[ sin ( 8 x ) ]}{x})

8

Solution steps

x \to 0 lim (\frac{[ sin ( 8 x ) ]}{x})

Simplify

= x \to 0 lim (\frac{sin ( 8 x )}{x})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{cos ( 8 x ) \cdot 8}{1})

Plug in the value

x = 0

= \frac{cos ( 8 \cdot 0 ) \cdot 8}{1}

Simplify

\frac{cos ( 8 \cdot 0 ) \cdot 8}{1} : 8

= 8

What is the limit as x approaches 0 of ([sin(8x)])/x ?
The limit as x approaches 0 of ([sin(8x)])/x is 8