The function f(x)=√1+x2−√1−x2x2 for x≠0;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+x2−√1−x2x2lefthandlimit=limitx→0−f(x)limitx→0−√1+x2−√1−x2x2×√1+x2+√1−x2√1+x2+√1−x2=limitx→0−1+x2−(1−x2)x2=limitx→0−2x2x2=2Righthandlimit=limitx→0+f(x)limitx→0+√1+x2−√1−x2x2×√1+x2+√1−x2√1+x2+√1−x2=limitx→0+1+x2−(1−x2)x2=limitx→0+2x2x2=2limitx→0−f(x)=limitx→0+f(x)≠f(0)