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Show that the function f given byf(x) ={:( x^(2)+5, if xne 0), (3, if x = 0):} |
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Answer» Solution :The function is defined at x =0 its VALUE at x =0 is 3 when `x ne 0`, the function is given by a polynomial, Hence, ` underset(x to 0) lim F(x) = underset(x to 0)lim x^(2)+5 =0^(2) + 5=5 ` Since the limit does notcoincide with f(0) , the function is not continuous at x =0, As well, x =0 is the only point of discontinuity . |
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