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})

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

d er i v a t i v e (8 x^{2} - 14 x) e^{x}

\int 1 + \frac{1}{x ^{2}} d x

\int - 4 x^{2} - 12 x + 16 d x

\int y - e^{c o s (x)} sin (x) d x

(x cos (x))^{^{'}}

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