alleryFor f(x) = sin(1/x) for x ≠ 0, what is the limit as x → 0?
ADoes not exist (oscillates infinitely many times)
B1
C0
DInfinity
Answer & Solution
Correct answer: A. Does not exist (oscillates infinitely many times)
As x → 0, 1/x → ∞, and sin oscillates between -1 and 1 infinitely often.
So the function has no specific limit.
(Compare with x × sin(1/x), which DOES have limit 0 by squeeze theorem.)
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