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The value of k for which `f(x) = {((sin 5x)/(3x)","," if " x !=0),(" k,"," if " x = 0):}` is contnuous at x = 0 isA. `(1)/(3)`B. 0C. `(3)/(5)`D. `(5)/(3)` |
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Answer» Correct Answer - D For continuity at `x = 0`, we must have `underset(x rarr 0)(lim) f(x) = f(0)` `underset(x rarr 0)(lim) f(x) = underset(x rarr 0)(lim) (sin 5x)/(5x) xx (5)/(3) = (5)/(3) underset(5x rarr 0)(lim) (sin 5x)/(5x) = ((5)/(3) xx 1) = (5)/(3)` `:.` we must have, `f(0) = (5)/(3) hArr k = (5)/(3)` |
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