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Unformatted text preview: (b) (5 points) Let f be the function f ( x ) = x 2-1 | x-1 | . Can you deﬁne f for x = 1 so that f is continuous at 1. Solution: For x > 1 we have f ( x ) = ( x + 1) x-1 | x-1 | = x + 1 while for x < 1 f ( x ) = ( x + 1) x-1 | x-1 | =-( x + 1) so that lim x → 1 + f ( x ) = 2 lim x → 1-f ( x ) =-2 Thus f ( x ) has a jump discontinuity at 1. There is no way to deﬁne f for x = 1 so that f is continuous at 1. Page 2 of 2...
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