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`lim_(x to (pi)/(2))(a^(cot x) -a^(cosx))/(cot x- cot x )` is equalt oA. `log a`B. `log 2`C. aD. log x |
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Answer» Correct Answer - A `underset(x to (x)/(2))(lim)((a^(cotx)-a^(cos x))/(cot x - cot x))` `=underset(x to (pi)/(2))(lim) a^(cosx)((a^(cot x - cos x) -1)/(cotx - cosx))` `=a^(cos.(pi)/(2))underset(x to (pi)/(2))(lim)(because underset(x to0)(lim) (a^(x)-1)/(x) = log a)` `= 1 log a = loga( because underset(x to0)(lim) (a^(x)-1)/(x) = log a)` |
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