What is the limit as x approaches 0 of (2sin(3x))/x ?

The limit as x approaches 0 of (2sin(3x))/x is 6

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limit as x approaches 0 of (2sin(3x))/x

x \to 0 lim (\frac{2 sin ( 3 x )}{x})

6

Solution steps

x \to 0 lim (\frac{2 sin ( 3 x )}{x})

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

= 2 \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})

= 2 \cdot x \to 0 lim (\frac{cos ( 3 x ) \cdot 3}{1})

Plug in the value

x = 0

= 2 \cdot \frac{cos ( 3 \cdot 0 ) \cdot 3}{1}

Simplify

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

= 6

\int \frac{1}{4 π t} e^{- \frac{r ^{2}}{4 t}} r d r

{\frac{1}{4 s ^{2} + 1}}

\int \frac{1}{4 + 5 x ^{2}} d x

\frac{\partial}{\partial y} (2 x y z^{2})

y^{^{''}} - 4 y^{^{'}} + 4 y = 6 e^{2 t} - 6 t e^{2 t} - 12 t + 12

What is the limit as x approaches 0 of (2sin(3x))/x ?
The limit as x approaches 0 of (2sin(3x))/x is 6