What is the limit as x approaches 0 of 3xsin(1/x) ?

The limit as x approaches 0 of 3xsin(1/x) is 0

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limit as x approaches 0 of 3xsin(1/x)

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

0

Solution steps

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

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

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

Apply the Squeeze Theorem:

0

= 3 \cdot 0

Simplify

= 0

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