InterviewSolution
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InterviewSolution
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Show that the funcation `f(x)={{:(x","," if x is an intger ") ,( 0",", " if x is not an integer "):}` is discontinuous at each integral value of x. |
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Answer» Let x= n when n is an integer. Then , f(n) =n ` lim_(x to n+) f(x) = lim_(h to 0) f( n +h) =0 ` [ ( n +h) is not an integer ` Rightarrrow ` f( n +h) =0] ` and lim_(x to n-) f(x)( = lim( h to 0) f( n -h) =0` [ ( n-h) is not an interger ` Rightarrow ` f ( n -h) =0] ` lim_(x to n +) f(x) = lim_( x to n-) f(x) =0 ` So, ` lim_( x to n) f(x) = 0 ne f( n)` Hence, f(x) is discontinuous at x = n |
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