What is the limit as x approaches 0 of (1-cos^2(3x))/(x^2) ?

The limit as x approaches 0 of (1-cos^2(3x))/(x^2) is 9

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limit as x approaches 0 of (1-cos^2(3x))/(x^2)

x \to 0 lim (\frac{1 - cos ^{2} ( 3 x )}{x ^{2}})

9

Solution steps

x \to 0 lim (\frac{1 - cos ^{2} ( 3 x )}{x ^{2}})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{3 sin ( 6 x )}{2 x})

= x \to 0 lim (\frac{3 sin ( 6 x )}{2 x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{18 cos ( 6 x )}{2})

= x \to 0 lim (\frac{18 cos ( 6 x )}{2})

Plug in the value

x = 0

= \frac{18 cos ( 6 \cdot 0 )}{2}

Simplify

\frac{18 cos ( 6 \cdot 0 )}{2} : 9

= 9

f (x) = 3 arcsin (x^{4})

\int_{0}^{1} 3 x^{2} d x

x \to - 2 lim (\frac{4 - x ^{2}}{x + 2})

\int 10 sinh (4 x - ln (2)) d x

\int ln (x) x d x

What is the limit as x approaches 0 of (1-cos^2(3x))/(x^2) ?
The limit as x approaches 0 of (1-cos^2(3x))/(x^2) is 9