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If f(x) = sqrt(1-(sqrt1-x^2)) , then ...

If `f(x) = sqrt(1-(sqrt1-x^2))` , then `f(x)` is (a)continuous on [-1, 1] and differentiable on (-1, 1) (b) continuous on [-1,1] and differentiable on `(-1, 0) uu (0, 1)` (C) continuous and differentiable on [-1, 1](d) none of these

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We have` f(0)=0`
L.H.L. =`lim​_(x->0^(-))f(x)=lim​_(x->0)sqrt(1−sqrt(1−x^2)) ​ ​=0`
R.H.L=`lim​_(x->0^(+))=lim​_(x->0)​sqrt(1−sqrt(1−x^2)) ​ ​=0`
Hence, both left hand and right hand limits are the same and equal to f(0).
Hence, f(x) is continuous at x=0
...
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