What is the limit as x approaches 0+of (5x)/(sin(x)) ?

The limit as x approaches 0+of (5x)/(sin(x)) is 5

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limit as x approaches 0+of (5x)/(sin(x))

x \to 0 + lim (\frac{5 x}{sin ( x )})

5

Solution steps

x \to 0 + lim (\frac{5 x}{sin ( x )})

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

= 5 \cdot x \to 0 + lim (\frac{x}{sin ( x )})

Apply L'Hopital's Rule

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

= 5 \cdot x \to 0 + lim (\frac{1}{cos ( x )})

Plug in the value

x = 0

= 5 \cdot \frac{1}{cos ( 0 )}

Simplify

5 \cdot \frac{1}{cos ( 0 )} : 5

= 5

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What is the limit as x approaches 0+of (5x)/(sin(x)) ?
The limit as x approaches 0+of (5x)/(sin(x)) is 5