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+1 vote
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in Continuity and Differentiability by (48.6k points)
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Prove that \(f(x) = \begin{cases} sin (1/x), & \quad \text{when } x ≠0 \text{}\\0, & \quad \text{when } x = 0 \text{} \end{cases} \) is discontinuous at x = 0.

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+1 vote
by (49.9k points) 1 flag
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Best answer

It is given that

\(f(x) = \begin{cases} sin (1/x), & \quad \text{when } x ≠0 \text{}\\0, & \quad \text{when } x = 0 \text{} \end{cases} \)

Consider left hand limit at x = 0

Therefore, f(x) is discontinuous at x = 0.

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