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If the function `f(x) = {(kx + 5 ", when " x le 2),(x -1 ", when " x gt 2):}` is continuous at x = 2 then k = ?A. 2B. `-2`C. 3D. `-3` |
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Answer» Correct Answer - B `f(2) = underset(x rarr 2)(lim) f(x)` `underset(x rarr 2^(+))(lim) f(x) = underset(h rarr 0)(lim) f(2 + h) = underset(h rarr 0)(lim) (2 + h -1) = 1` `underset(x rarr 2)(lim) f(x) = underset(h rarr 0)(lim) f(2 -h) = underset(h rarr 0)(lim){k (2 -h) + 5} = 2k + 5` `:. 2k + 5 = 1 rArr k == -2` Also, `f(2) = 2k + 5 = 1`. Hence, `k = -2` |
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