InterviewSolution
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InterviewSolution
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If `f(x)=lim_(nrarroo)((x^(2)+ax+1)+x^(2n)(2x^(2)+x+b))/(1+x^(2n)) and lim_(xrarrpm1)f(x)` exists, then The value of b isA. `-1`B. 1C. 0D. 2 |
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Answer» Correct Answer - C `f(x)=underset(nrarroo)(lim)((x^(2)+ax+1)+x^(2n)(2x^(2)+x+b))/(1+x^(2n))` `={{:(x^(2)+ax+1",",|x|lt1),(2x^(2)+x+b",",|x|gt1),((-a+b+3)/(2)",",x=-1),((a+b+5)/(2)",",x=1):}` `underset(xrarr-1)(lim)f(x)" exists if"` `underset(xrarr -1)(lim)f(x)=underset(xrarr-1^(+))(lim)f(x)` `rArr" "underset(xrarr-1^(-))(lim)(2x^(2)+x+b)=underset(xrarr-1^(+))(lim)(x^(2)+ax+1)` `rArr" "2-1+b=1-a+1` `rArr" "a+b=1" (i)"` `underset(xrarr1)(lim)f(x)" exists if"` `underset(xrarr1^(-))(lim)f(x)=underset(xrarr1^(+))(lim)f(x)` `rArr" "underset(xrarr1^(-))(lim)(x^(2)+ax+1)=underset(xrarr1^(+))(lim)(2x^(2)+x+b)` `rArr 1+a+1=2+1+b` `rArr a-b=1" (ii)"` `"Solving Eqs. (i) and (ii), we get a = 1 and b=0."` |
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