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Let `f(x) = {(x "sin "(1)/(x)","," if " x != 0),(" 0,"," where " x = 0):}` Then, which of the following is the true statement ?A. f(x) is not defined at x = 0B. `underset(x rarr 0)(lim) f(x)` does not existC. f(x) is continuous at x = 0D. `f(x)` is discontinuous at x = 0 |
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Answer» Correct Answer - C `f(0) = 0` `underset(x rarr 0)(lim) f(x) = underset(x rarr 0)(lim) x "sin " (1)/(x) = 0 xx ("a finite quantity") = 0` `:. f(x)` is continuous at `x = 0` |
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