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

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

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

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

x \to - 3 lim (2 x^{3} + 3 x^{2} - 11)

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

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