InterviewSolution
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InterviewSolution
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Given a real valued function f such that `f(x)={tan^2[x]/(x^2-[x]^2) , x lt 0 and 1 , x=0 and sqrt({x}cot{x}) , x lt 0` where [.] represents greatest integer function thenA. `p_(1)" ln "a_(1)+p_(2)" ln "a_(2)+...+p_(n)" ln "a_(n)`B. `a_(1)^(p_(1))+a_(2)^(p_(2))+...+a_(n)^(p_(n))`C. `a_(1)^(p_(1)).a_(2)^(p_(2))...a_(n)^(p_(n))`D. `sum_(r=1)^(n)a_(r)p_(r)` |
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Answer» Correct Answer - A::B::C::D We have `f(x)=underset(xto0^(+))lim(tan^(2){x})/((x^(2)-[x]^(2)))=underset(xto0^(+))lim(tan^(2)x)/(x^(2))=1" "(1)` `(becausexto0^(+),[x]=0implies{x}=x)` Also, `underset(xto0^(-))limf(x)=underset(xto0^(-))limsqrt({x}cot{x})=sqrt(cot1)" "(2)` `(becausexto0^(-),[x]=-1implies{x}=x+1implies{x}to1)` Also,`cot^(-1)(underset(xto0^(-))limf(x))^(2)=cot^(-1)(cot1)=1.` Also, `tan^(-1)(underset(xto0^(+))limf(x))=tan^(-1)1=(pi)/(4)` |
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