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Question
Consider the function `f(x) = x sin pi/x`. What value must we give f(0) in order to make the function continuous everywhere?
Solution
`f(x) = x sin pi/x`
Define f(x) on R as
`f(x) = {{:(x sin pi/x, "if" x ≠ 0),(0, "if" x = 0):}`
∴ f(0) = 0.
Then f(x) is continuous on R.
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