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

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

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

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

0

Solution steps

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

Simplify

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

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

Apply L'Hopital's Rule

: x \to 0 + lim (\frac{cos ( x ^{2} ) \cdot 2 x}{1})

= x \to 0 + lim (\frac{cos ( x ^{2} ) \cdot 2 x}{1})

Plug in the value

x = 0

= \frac{cos ( 0 ^{2} ) \cdot 2 \cdot 0}{1}

Simplify

\frac{cos ( 0 ^{2} ) \cdot 2 \cdot 0}{1} : 0

= 0

\int_{0}^{π} x \cdot sin (x) d x

n = 1 \sum \infty 3^{- 2 - 2 n} \cdot 2^{3 n + 1}

\frac{\partial}{\partial x} (\frac{x}{2 2})

\int 3 - 2 x x^{2} d x

x = 7 y^{2}, x = 5 + 2 y^{2}

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