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) sin (\frac{1}{x}))

0

Solution steps

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

Apply the Squeeze Theorem:

0

= 0

x \to - 7 lim (\frac{x ^{2} - 3}{7 - x})

8 (x - \frac{1}{x})^{3}

\int 6 x^{2} - 8 x + 3 d x

x^{3} (3 - x)^{4}

\int 1 + (\frac{1}{x ^{\frac{1}{3}}})^{2} d x

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