What is the limit as x approaches 0 of (6sin(3x))/x ?

The limit as x approaches 0 of (6sin(3x))/x is 18

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limit as x approaches 0 of (6sin(3x))/x

x \to 0 lim (\frac{6 sin ( 3 x )}{x})

18

Solution steps

x \to 0 lim (\frac{6 sin ( 3 x )}{x})

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

= 6 \cdot x \to 0 lim (\frac{sin ( 3 x )}{x})

Apply L'Hopital's Rule

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

= 6 \cdot x \to 0 lim (\frac{cos ( 3 x ) \cdot 3}{1})

Plug in the value

x = 0

= 6 \cdot \frac{cos ( 3 \cdot 0 ) \cdot 3}{1}

Simplify

6 \cdot \frac{cos ( 3 \cdot 0 ) \cdot 3}{1} : 18

= 18

\frac{d}{d x} (3^{2 x^{2}} x)

\int_{t}^{2} (\frac{1}{x - 1}) d x

\int 3^{2} d x

f (x) = e^{\frac{z}{( z - 2 )}}

\int \frac{1}{( 3 x + 1 ) ^{4}} d x

What is the limit as x approaches 0 of (6sin(3x))/x ?
The limit as x approaches 0 of (6sin(3x))/x is 18