What is the limit as x approaches 0-of x*sin(1/x) ?

The limit as x approaches 0-of x*sin(1/x) is 0

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limit as x approaches 0-of x*sin(1/x)

x \to 0 - lim (x \cdot sin (\frac{1}{x}))

0

Solution steps

x \to 0 - lim (x sin (\frac{1}{x}))

Apply the Squeeze Theorem:

0

= 0

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\int \frac{5 x}{( x ^{2} + 2 ) ^{2}} d x

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What is the limit as x approaches 0-of x*sin(1/x) ?
The limit as x approaches 0-of x*sin(1/x) is 0