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

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

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

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

0

Solution steps

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

Simplify

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

Apply the Squeeze Theorem:

0

= 0

x \to 1 lim (\frac{x ^{4} + x ^{2} - 2}{x ^{2} + 2 x - 3})

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

x \to 0 lim (2 e^{x} cos (x))

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

x \to 0 lim (tan (sin (x)))

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