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

t^{2} \cdot e^{3 t}

\int t cos (t) d t

ln (x^{3})

\int \frac{x ^{2}}{2 + x ^{6}} d x

(- 14, - 11), (- 12, 11)

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