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

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

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limit as n approaches 0 of 1/n sin(1/n)

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

diverges

Solution steps

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

Simplify

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

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

Apply Limit Divergence Criterion:

diverges

= diverges

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