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

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

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

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

0

Solution steps

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

Apply the Squeeze Theorem:

0

= 0

x \to 2 lim (x^{3} + 5 x^{2} - 5 x + 3)

x \to 0 lim (\frac{ln ( cos ( 3 x ) )}{ln ( cos ( 5 x ) )})

h \to 0 lim (\frac{( 2 + h ) ^{5} - 32}{h})

x \to - \infty lim (x^{2 n})

x \to \infty lim (\frac{2}{+ x})

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