What is the limit as x approaches 0 of xsin(1/(x^3)) ?

The limit as x approaches 0 of xsin(1/(x^3)) is 0

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limit as x approaches 0 of xsin(1/(x^3))

x \to 0 lim (x sin (\frac{1}{x ^{3}}))

0

Solution steps

x \to 0 lim (x sin (\frac{1}{x ^{3}}))

Apply the Squeeze Theorem:

0

= 0

x \to - \infty lim (x e^{x} + 1)

x \to 0 lim ((a^{x} - 1)^{x})

x \to 6 lim (10)

x \to - 2 lim (\frac{x + 1}{6 x - 3})

x \to 0 lim (\frac{2 - x}{1 + x})

What is the limit as x approaches 0 of xsin(1/(x^3)) ?
The limit as x approaches 0 of xsin(1/(x^3)) is 0