What is the limit as x approaches 0 of 3x^n*sin(2/x) ?

The limit as x approaches 0 of 3x^n*sin(2/x) is 0

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limit as x approaches 0 of 3x^n*sin(2/x)

x \to 0 lim (3 x^{n} \cdot sin (\frac{2}{x}))

0

Solution steps

x \to 0 lim (3 x^{n} sin (\frac{2}{x}))

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 3 \cdot x \to 0 lim (x^{n} sin (\frac{2}{x}))

Apply the Squeeze Theorem:

0

= 3 \cdot 0

Simplify

= 0

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What is the limit as x approaches 0 of 3x^n*sin(2/x) ?
The limit as x approaches 0 of 3x^n*sin(2/x) is 0