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If the function `f(x) = {((sin^(2)ax)/(x^(2))","," when "x != 0),(" k,"," when " x = 0):}`is continuous at x = 0 then k = ?A. aB. `a^(2)`C. `-2`D. `-4` |
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Answer» Correct Answer - B `underset(x rarr 0)(lim) f(x) = underset(x rarr 0)(lim) (sin^(2) ax)/(a^(2) x^(2)) xx a^(2) = a^(2). underset(ax rarr 0)(lim) ((sin ax)/(ax))^(2) = a^(2) xx 1^(2) = a^(2)` For continuity, we must have `f(0) = a^(2)` |
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