Why does the limit as x approaches zero for the function f (x) = sin (π/x) not exist?

limx→0 sin (π/x)

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Mathematics

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30 December, 04:10

Why does the limit as x approaches zero for the function f (x) = sin (π/x) not exist?

limx→0 sin (π/x)

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Whitney Williamson · Answer 1

As x approaches 0, pi/x approaches infinity

that would be sin (infinty) which is nonexistant because it goes up and down and doesn't approache a value

Why does the limit as x approaches zero for the function f (x) = sin (π/x) not exist?limx→0 sin (π/x)

Why does the limit as x approaches zero for the function f (x) = sin (π/x) not exist?

limx→0 sin (π/x)