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

\int x^{2} + 14 x d x

y = 2 x^{3} - 3 x^{2}

y^{^{''}} + 2 y = 0, y (0) = 1, y (1) = 0

y = arccot (t)

y^{^{''}} + 200 y^{^{'}} + 10 y = 100

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