What is the limit as x approaches 0 of (xsin(1/x))/x ?

The limit as x approaches 0 of (xsin(1/x))/x is diverges

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limit as x approaches 0 of (xsin(1/x))/x

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

diverges

Solution steps

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

Cancel the common factor:

x

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

Apply Limit Divergence Criterion:

diverges

= diverges

\frac{d}{d x} (x^{3} - \frac{1}{x})

x \to 0 lim (x cos (x^{2}))

\int x \cdot (x^{2} + 1)^{2} d x

\frac{\partial}{\partial x} (x - x^{2} y)

\frac{d}{d x} (\frac{sin ( 2 x )}{4})

What is the limit as x approaches 0 of (xsin(1/x))/x ?
The limit as x approaches 0 of (xsin(1/x))/x is diverges