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

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

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limit as x approaches 0 of sin^2(x)(1/x)

x \to 0 lim (sin^{2} (x) (\frac{1}{x}))

0

Solution steps

x \to 0 lim (sin^{2} (x) \frac{1}{x})

Simplify

sin^{2} (x) \frac{1}{x} : \frac{sin ^{2} ( x )}{x}

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{sin ( 2 x )}{1})

= x \to 0 lim (\frac{sin ( 2 x )}{1})

Plug in the value

x = 0

= \frac{sin ( 2 \cdot 0 )}{1}

Simplify

\frac{sin ( 2 \cdot 0 )}{1} : 0

= 0

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

n = 0 \sum \infty \frac{6}{5 ^{n}}

\int 2 sec (2 x) tan (2 x) d x

y^{^{'}} + (\frac{1}{x}) y = 8 x^{2}

\int_{2}^{4} x^{2} y + y^{2} x + x + y d x

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