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

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

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

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

3

Solution steps

x \to 0 lim (\frac{3 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

\int (x + 1) (x - x + 1) d x

\int t cos (t^{2}) d t

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

f (x) = (\frac{1}{2 x + 3})^{3}

\frac{8}{x ^{2} + 4} (2.1)

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