What is the limit as x approaches 0 of ((sin(9x)))/x ?

The limit as x approaches 0 of ((sin(9x)))/x is 9

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limit as x approaches 0 of ((sin(9x)))/x

x \to 0 lim (\frac{( sin ( 9 x ) )}{x})

9

Solution steps

x \to 0 lim (\frac{sin ( 9 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( 9 x ) \cdot 9}{1})

= x \to 0 lim (\frac{cos ( 9 x ) \cdot 9}{1})

Plug in the value

x = 0

= \frac{cos ( 9 \cdot 0 ) \cdot 9}{1}

Simplify

\frac{cos ( 9 \cdot 0 ) \cdot 9}{1} : 9

= 9

f (x) = (x^{2} + 9 x + 2)^{5}

f (x) = 2 e^{x} + 10 x, at x = 0

\frac{d}{d x} (\frac{x + 1}{x})

x \to + 2 lim (2 x)

\int sin^{4} (3 x) cos^{3} (3 x) d x

What is the limit as x approaches 0 of ((sin(9x)))/x ?
The limit as x approaches 0 of ((sin(9x)))/x is 9