What is the limit as x approaches 0 of (sin^2(6x))/x ?

The limit as x approaches 0 of (sin^2(6x))/x is 0

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limit as x approaches 0 of (sin^2(6x))/x

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

0

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{12 sin ( 6 x ) cos ( 6 x )}{1})

= x \to 0 lim (\frac{12 sin ( 6 x ) cos ( 6 x )}{1})

Plug in the value

x = 0

= \frac{12 sin ( 6 \cdot 0 ) cos ( 6 \cdot 0 )}{1}

Simplify

\frac{12 sin ( 6 \cdot 0 ) cos ( 6 \cdot 0 )}{1} : 0

= 0

x \to \infty lim (2 x^{x})

y^{^{''}} + 3 y^{^{'}} = 0, y (0) = 9, y^{^{'}} (0) = - 6

n = 1 \sum \infty n (1 - p)^{n - 1}

9 x, x^{2} - 10, 0

\int e^{6 x} x^{3} d x

What is the limit as x approaches 0 of (sin^2(6x))/x ?
The limit as x approaches 0 of (sin^2(6x))/x is 0