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Question

Let fx=x+1,if x0x-1,if x<0Prove that limx0 fx does not exist.

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Solution

fx=x+1,x0x-1,x<0LHL:limx0- fx=limx0- x-1Let x=0-h, where h0.limh0 0-h-1=-1RHL:limx0+ fx=limx0+ x+1Let x=0+h, where h0.limh0 0+h+1=+1
LHL ≠ RHL
Thus, limx0 fx does not exist.

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