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

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

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

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

\frac{9}{5}

Decimal

1.8

Solution steps

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

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

= \frac{1}{5} \cdot x \to 0 lim (\frac{sin ^{2} ( 3 x )}{x ^{2}})

Apply L'Hopital's Rule

= \frac{1}{5} \cdot x \to 0 lim (\frac{3 sin ( 6 x )}{2 x})

Apply L'Hopital's Rule

= \frac{1}{5} \cdot x \to 0 lim (\frac{18 cos ( 6 x )}{2})

Plug in the value

x = 0

= \frac{1}{5} \cdot \frac{18 cos ( 6 \cdot 0 )}{2}

Simplify

\frac{1}{5} \cdot \frac{18 cos ( 6 \cdot 0 )}{2} : \frac{9}{5}

= \frac{9}{5}

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