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})

Apply L'Hopital's Rule

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

= 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

x \to 2 lim (8 x^{3} + 1)

8 e^{8 t + 5}

\int \frac{1}{5 - 8 x} d x

x \to 2 lim (2 x - 1)

(x^{2} + 1)^{^{'}}

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