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InterviewSolution
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If `alpha`is an integer satisfying `|alpha|lt=4-|[x]|,`where `x`is a real number for which `2xtan^(-1)x`is greater than or equal to `ln(1+x^2),`then the number of maximum possible values of `a`(where [.] represents the greatest integer function) is_____ |
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Answer» Correct Answer - 9 (9) Let y =2x `tan^(-1)x-ln(1+x^(2))` `y=2 tan^(-1)x+(2x)/(1+x^(2))-(2x)/(1+x^(2))` `therefore y gt 0 forall lx in R^(+) ,y lt0 forall x in R^(-)` Therefore 4-|[x]| takes the values 0,1,2,3,4 `|alpha|le4-|[x]|` is satisfied by`alpha=0 pm1,pm 2,pm 3,pm 4` Therefore number of values of `alpha` is 9 |
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