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Let `f(x)={(0 , x "is irrational"),(2/(2q^(3)-q^(2)+q+sin^(2)q+5) , if x=p/q ("rational")):}` (where HCF `(p,q)=1,p,q,gt0`) and `f(x)` is defined `AAxgt0` then which of the following is/are incorrect?A. `f(x)` is continuous at each irrational in `(0,oo)`B. `f(x)` is continuous at each rational in `(0,oo)`C. `f(x)` is discontinuous at each rational in `(0,oo)`D. `f(x)` is discontinuous for all `x` in `(0,oo)` |
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Answer» Correct Answer - B::D Let `x=sqrt(3)` `f(sqrt(3))=0` `because sqrt(3)=1.732050807`………. As the decimal part increase then in the expression `p/q, q` becomes very large So, `2/(2q^(3)-q^(2)+q+sin^(2)q+t)to0` Hence `lim_(xtosqrt(3))f(x)=0` Thus, `f(x)` is continuous at each irrational |
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