What is the limit as x approaches 0 of (x^2)/(sin^2(7x)) ?

The limit as x approaches 0 of (x^2)/(sin^2(7x)) is 1/49

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limit as x approaches 0 of (x^2)/(sin^2(7x))

x \to 0 lim (\frac{x ^{2}}{sin ^{2} ( 7 x )})

\frac{1}{49}

Decimal

0.02040 \dots

Solution steps

x \to 0 lim (\frac{x ^{2}}{sin ^{2} ( 7 x )})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{2 x}{14 sin ( 7 x ) cos ( 7 x )})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{2}{98 cos ( 14 x )})

Plug in the value

x = 0

= \frac{2}{98 cos ( 14 \cdot 0 )}

Simplify

\frac{2}{98 cos ( 14 \cdot 0 )} : \frac{1}{49}

= \frac{1}{49}

What is the limit as x approaches 0 of (x^2)/(sin^2(7x)) ?
The limit as x approaches 0 of (x^2)/(sin^2(7x)) is 1/49