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Question

Check continuity f(x)=|x|+1,x<00,x=0|x|+1,x>0

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Solution

at x=0
R.H.L limx0+hf(x)
=limh0|h|+1
=limh0h+1
=1
L.H.L limx0hf(x)
=limh0|h|+1
=limh0h+1
=1
and f(0)=0
Since R.H.L = L.H.L
so, limit exist at x=0
since R.H.l = L.H.L f(0)
Therefore f(x) is not continuous at x=0

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