InterviewSolution
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InterviewSolution
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The value of a and b such that the function `f(x)={(-2sinx"," , -pi le x le -(pi)/(2)),(a sinx+b",", -(pi)/(2) lt x lt (pi)/(2)),(cosx",", (pi)/(2) le x le pi ):}` is continuous in `[-pi,pi]` areA. `-1,0`B. `1,0`C. 1,1D. `-1,1` |
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Answer» Correct Answer - D For continuity in `[-pi , pi]` , we must have At `x = - ""(pi)/(2) , f (-""(pi)/(2)) = underset(x to (-""(pi)/(2))^(-)) ("lim") (-2 sin x )` `= underset( x to (-""(pi)/(2))^(+)) (a sin x + b)` `implies 2 = - a + b " " … (i) ` At `x = pi/2 ,` `f((pi)/(2)) = underset(x to ((pi)/(2))^(-)) ("lim") ( asin x + b) = underset( x to ((pi)/(2))^(+)) ("lim") cos x` `implies 0 = a + b " " .... (ii)` On solving Eqs. (i) and (ii) we get , `a = -1 , b = 1` |
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