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Question

Find limx1f(x), where f(x)= {x21, x1x21, x>1

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Solution

f(x)={x21, x1x21, x>1
L.H.L =limx1f(x)=limx1[x21]=121=11=0
R.H.L =limx1+f(x)=limx1[x21]=121=11=2
Clearly L.H.L R.H.L
Hence limx1f(x) does not exist.

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