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

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

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

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

6

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= 6

\int \frac{x ^{2} + 9}{x} d x

\frac{d}{d x} (\frac{1}{9} (x^{2} + 6)^{\frac{3}{2}})

y^{^{'}} + \frac{1}{x} y = 9 x^{2}

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

3 x, x

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