What is the limit as x approaches 0+of (9x)/(sin(x)) ?

The limit as x approaches 0+of (9x)/(sin(x)) is 9

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limit as x approaches 0+of (9x)/(sin(x))

x \to 0 + lim (\frac{9 x}{sin ( x )})

9

Solution steps

x \to 0 + lim (\frac{9 x}{sin ( x )})

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

= 9 \cdot x \to 0 + lim (\frac{x}{sin ( x )})

Apply L'Hopital's Rule

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

= 9 \cdot x \to 0 + lim (\frac{1}{cos ( x )})

Plug in the value

x = 0

= 9 \cdot \frac{1}{cos ( 0 )}

Simplify

9 \cdot \frac{1}{cos ( 0 )} : 9

= 9

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What is the limit as x approaches 0+of (9x)/(sin(x)) ?
The limit as x approaches 0+of (9x)/(sin(x)) is 9