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

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

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

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

8

Solution steps

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

Apply L'Hopital's Rule

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

Plug in the value

x = 0

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

Simplify

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

= 8

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