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Question

The function f(x)=1+x21x2x2 for x0; f(0)=1 at x=0 is

A
continuous
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B
discontinuous
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C
not determined
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D
none
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Solution

The correct option is A discontinuous
f(x)=1+x21x2x2lefthandlimit=limitx0f(x)limitx01+x21x2x2×1+x2+1x21+x2+1x2=limitx01+x2(1x2)x2=limitx02x2x2=2Righthandlimit=limitx0+f(x)limitx0+1+x21x2x2×1+x2+1x21+x2+1x2=limitx0+1+x2(1x2)x2=limitx0+2x2x2=2limitx0f(x)=limitx0+f(x)f(0)
So this function is discontinuous at x=0
Correct option is B

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