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

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

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

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

diverges

Solution steps

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

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

With the exception of indeterminate form

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

x \to 0 lim (g (x)) = g (0)

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

diverges

= g \cdot 0 diverges

= diverges

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