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B
Continuous on [−1,1] and differentiable on (−1,0)∪(0,1)
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C
Continuous and differentiable on [−1,1]
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D
Continuous and differentiable on (−1,1)
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Solution
The correct option is A Continuous on [−1,1] and differentiable on (−1,1) f(x)=√1−√1−x2forx∈(−1,1)letx=sin(t)fort∈(−π2,π2)f(t)=√1−cos(t)=√2sin(t/2)Theabovefunctioniscontinuousaswellasdifferentiableforx∈(−1,1) Hence, the answer is "A"