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

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

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

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

0

Solution steps

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

Apply the Squeeze Theorem:

0

= 0

\int 1 + \frac{1}{4} x d x

(2.4) (3.6)

\frac{d}{d x} (ln (8 x^{2} + 1))

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

n = 0 \sum \infty 3^{n} x^{2 n}

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