What is the limit as x approaches 0 of x^4*sin(1/x) ?

The limit as x approaches 0 of x^4*sin(1/x) is 0

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limit as x approaches 0 of x^4*sin(1/x)

x \to 0 lim (x^{4} \cdot sin (\frac{1}{x}))

0

Solution steps

x \to 0 lim (x^{4} sin (\frac{1}{x}))

Apply the Squeeze Theorem:

0

= 0

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

x \to - 3 lim (ln (4 x + 14))

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

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

x \to 0 lim (\frac{x}{[ x ]})

What is the limit as x approaches 0 of x^4*sin(1/x) ?
The limit as x approaches 0 of x^4*sin(1/x) is 0