What is the limit as x approaches 0 of (sin^2(3x))/(sin^2(5x)) ?

The limit as x approaches 0 of (sin^2(3x))/(sin^2(5x)) is 9/25

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limit as x approaches 0 of (sin^2(3x))/(sin^2(5x))

x \to 0 lim (\frac{sin ^{2} ( 3 x )}{sin ^{2} ( 5 x )})

\frac{9}{25}

Decimal

0.36

Solution steps

x \to 0 lim (\frac{sin ^{2} ( 3 x )}{sin ^{2} ( 5 x )})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{3 sin ( 6 x )}{5 sin ( 10 x )})

= x \to 0 lim (\frac{3 sin ( 6 x )}{5 sin ( 10 x )})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{18 cos ( 6 x )}{50 cos ( 10 x )})

= x \to 0 lim (\frac{18 cos ( 6 x )}{50 cos ( 10 x )})

Plug in the value

x = 0

= \frac{18 cos ( 6 \cdot 0 )}{50 cos ( 10 \cdot 0 )}

Simplify

\frac{18 cos ( 6 \cdot 0 )}{50 cos ( 10 \cdot 0 )} : \frac{9}{25}

= \frac{9}{25}

x \to 0 lim (x^{4} + 3 x^{3} - x)

x \to 0 + lim (x \cdot sin (ln (x)))

x \to 2 lim (\frac{1}{x} - \frac{1}{2})

x \to 1 lim (\frac{x ^{x} - 1}{x \cdot ln ( x )})

x \to \infty lim (sin (2))

What is the limit as x approaches 0 of (sin^2(3x))/(sin^2(5x)) ?
The limit as x approaches 0 of (sin^2(3x))/(sin^2(5x)) is 9/25