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

The limit as x approaches 0 of (3sin(3x))/x is 9

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

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

9

Solution steps

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

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

= 3 \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})

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

Plug in the value

x = 0

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

Simplify

3 \cdot \frac{cos ( 3 \cdot 0 ) \cdot 3}{1} : 9

= 9

x, sin (x), [\frac{π}{2}, π]

y^{^{''}} + 3 y = 1

(x y - y) d y - (y + 1) d x = 0

\int sin (x) cos^{2} (x) + sin^{3} (x) d x

\frac{\partial}{\partial y} (\frac{e ^{2 - x}}{y ^{2}})

What is the limit as x approaches 0 of (3sin(3x))/x ?
The limit as x approaches 0 of (3sin(3x))/x is 9