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The value of x for which `f(x)=(sin.({x})/({x})+cos.({x})/({x}))` is maximum ({x} and [x] denots fractiona part and greatest integer part of x respectively)A. `1+(pi)/(4)`B. `2+(pi)/(4)`C. `1-(pi)/(4)`D. none of these |
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Answer» Correct Answer - A Let `({x})/([x])=alpha` `rArrf(x)= sin alpha + cos alpha` `" " =sqrt(2)(sin((pi)/(4)+alpha))` f(x) is maximum at `alpha(pi)/(4)` `:. ({x})/([x])=(pi)/(4)` `rArr {x}=(pi)/(4)[x]` is true at [x]=1 `:. {x}=(pi)/(4)` So `x=[x]+{x}=1+(pi)/(4)` |
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