What is the limit as x approaches 0 of (1-cos(3x))/x ?

The limit as x approaches 0 of (1-cos(3x))/x is 0

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limit as x approaches 0 of (1-cos(3x))/x

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

0

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{3 sin ( 3 x )}{1})

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

Plug in the value

x = 0

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

Simplify

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

= 0

\frac{d y}{d x}, 9 e^{x y} + 4 x^{2} - 2 y^{2} = 36

ln (\frac{4 x + 1}{x ^{2} - 2})

\int \frac{2 - sin ( x )}{2 + cos ( x )} d x

cos (3 x)

\int 60 d x

What is the limit as x approaches 0 of (1-cos(3x))/x ?
The limit as x approaches 0 of (1-cos(3x))/x is 0