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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? |
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Answer» `f(x)` is continuous at each irrational in `(0,oo)` `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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