What is the limit as x approaches 0 of (6x)/(sin(x)) ?

The limit as x approaches 0 of (6x)/(sin(x)) is 6

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limit as x approaches 0 of (6x)/(sin(x))

x \to 0 lim (\frac{6 x}{sin ( x )})

6

Solution steps

x \to 0 lim (\frac{6 x}{sin ( x )})

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

= 6 \cdot x \to 0 lim (\frac{x}{sin ( x )})

Apply L'Hopital's Rule

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

= 6 \cdot x \to 0 lim (\frac{1}{cos ( x )})

Plug in the value

x = 0

= 6 \cdot \frac{1}{cos ( 0 )}

Simplify

6 \cdot \frac{1}{cos ( 0 )} : 6

= 6

f (x) = x^{2} - 7, (4, 9)

\frac{( s + 1 )}{( s ^{2} + 4 s + 20 )}

x \to - \infty lim (\frac{4 + 5 e ^{4 x}}{5 - 6 e ^{5 x}})

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

\frac{d}{d x} y - \frac{1}{cos ( x )} = 0

What is the limit as x approaches 0 of (6x)/(sin(x)) ?
The limit as x approaches 0 of (6x)/(sin(x)) is 6