InterviewSolution
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InterviewSolution
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Show that the funcation `f(x)={{:(3x-2",", " when ", x le0),(x+1",", " when ", x gt 0):}` is discontinuous at x =0 |
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Answer» we have ` f(0) = (3 xx 0-2) = -2` ` lim_(x to 0+) f(x) = lim_(h to 0) f( 0+h)` ` lim_(h to 0) ( h+1) =1` ` lim_(x to 0-) f(x) = lim_(h to 0) f( 0-h)` ` lim_(h to 0) [ 3 (-h) -2] = lim_( h to 0) (-3 h-2) = -2` ` lim_(x to 0 +) f(x) ne lim_( x to 0-) f(x) and " therefore, " lim_(x to 0) f(x) ` does not exist. Hence, f(x) is discontinuous at x=0 |
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