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

\int 18 cos^{2} (x) sin (x) d x

x \to 0 lim (\frac{3 - 5 x}{4 x})

\int \frac{13}{x ^{2} + 1} d x

\frac{d y}{d x} = 3 y e^{x + 8}

x \to \infty lim ((- 1)^{x} \cdot (1 - \frac{1}{x ^{2}}))

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