What is the limit as x approaches 0 of (sin^2(8x))/x ?

The limit as x approaches 0 of (sin^2(8x))/x is 0

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limit as x approaches 0 of (sin^2(8x))/x

x \to 0 lim (\frac{sin ^{2} ( 8 x )}{x})

0

Solution steps

x \to 0 lim (\frac{sin ^{2} ( 8 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{16 sin ( 8 x ) cos ( 8 x )}{1})

= x \to 0 lim (\frac{16 sin ( 8 x ) cos ( 8 x )}{1})

Plug in the value

x = 0

= \frac{16 sin ( 8 \cdot 0 ) cos ( 8 \cdot 0 )}{1}

Simplify

\frac{16 sin ( 8 \cdot 0 ) cos ( 8 \cdot 0 )}{1} : 0

= 0

k \to \infty lim (ln (k))

x \to 1 lim (\frac{12}{x + 9})

x \to \frac{1}{4} lim (3 4 x + 8)

x \to - 5 lim ((x^{2} + 1)^{\frac{1}{3}})

x \to 0 lim (x^{2} + 2 x - 4)

What is the limit as x approaches 0 of (sin^2(8x))/x ?
The limit as x approaches 0 of (sin^2(8x))/x is 0