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 tan^{2} (x) d x

f (x) = (1 + x)^{- \frac{6}{5}}

x \to 3 lim (\frac{5 \cdot 4 ^{x}}{9 ^{x}})

\int cot (x) csc^{3} (x) d x

\frac{d}{d x} (x ln (6 x))

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