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}) 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

x \to 0 lim (\frac{x}{[ x ]})

x \to 0 + lim (4 (cot (x) - \frac{1}{x}))

x \to 0 lim (\frac{2 x - 5 x ^{2}}{x})

t \to 12 + lim (f (t))

x \to - 2 lim (62 x^{5})

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