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

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

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

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

diverges

Solution steps

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

Simplify

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

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

Apply Limit Divergence Criterion:

diverges

= diverges

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