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

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

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

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

3

Solution steps

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})

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

Plug in the value

x = 0

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

Simplify

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

= 3

x^{2} y^{^{''}} - 5 x y^{^{'}} + 9 y = 0

x \to 2 lim (x^{2} - 7 x + 5)

\frac{\partial}{\partial x} (\frac{1}{x ^{2} + y ^{2} + 1})

\int_{0}^{1} x e^{- 8 x^{2}} d x

\frac{d y}{d x} + 9 y = 3

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