What is the limit as x approaches 0 of 3(x/(sin(x))) ?

The limit as x approaches 0 of 3(x/(sin(x))) is 3

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limit as x approaches 0 of 3(x/(sin(x)))

x \to 0 lim (3 (\frac{x}{sin ( x )}))

3

Solution steps

x \to 0 lim (3 \cdot \frac{x}{sin ( x )})

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

= 3 \cdot x \to 0 lim (\frac{x}{sin ( x )})

Apply L'Hopital's Rule

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

= 3 \cdot x \to 0 lim (\frac{1}{cos ( x )})

Plug in the value

x = 0

= 3 \cdot \frac{1}{cos ( 0 )}

Simplify

3 \cdot \frac{1}{cos ( 0 )} : 3

= 3

x \to π - lim (\frac{cos ( x )}{x})

x \to 0 lim (x^{2} + cos (x))

n \to \infty lim (n a^{n})

x \to - 4 lim (x^{2} - 3 x + 12)

x \to 4 lim (6 x + 5)

What is the limit as x approaches 0 of 3(x/(sin(x))) ?
The limit as x approaches 0 of 3(x/(sin(x))) is 3