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

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

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

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

0

Solution steps

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

Apply the Squeeze Theorem:

0

= 0

x \to 2 lim (\frac{x}{4 - x ^{2}})

x \to 2 lim (9 x^{2} - 2 x)

x \to 0 lim (\frac{x}{1 + ∣ x ∣})

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

x \to 3 lim (3 x + 1)

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