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

If f(x)=sqrt(1-sqrt(1-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 ) ∪ ( 0 , 1 ) (c) continuous and differentiable on [-1, 1] (d) none of these

f(x) ={{:(1-sqrt(1-x^(2)),if -1lexle1),(1+ log ""(1)/(x), if xgt1):} (a) continuous and differentiable at x=1 (b) continuous but not differentiable at x=1 (c) neither continuous nor differentiable at x=1 (d) none of these

If f(x)={(1-cosx)/(xsinx),x!=0 and 1/2,x=0 then at x=0,f(x) is (a)continuous and differentiable (b)differentiable but not continuous (c)continuous but not differentiable (d)neither continuous nor differentiable

If f(x)={(1-cosx)/(xsinx),x!=0 and 1/2,x=0 then at x=0,f(x) is (a)continuous and differentiable (b)differentiable but not continuous (c)continuous but not differentiable (d)neither continuous nor differentiable

If f(x)=|(log)_e|x|| , then (a) f(x) is continuous and differentiable for all x in its domain] (b) f(x) is continuous for all x in its domain but not differentiable at x=+-1 (c) f(x) is neither continuous nor differentiable at x=+-1 (d) none of these

The function f(x)=|cosx| is (a) everywhere continuous and differentiable (b) everywhere continuous but not differentiable at (2n+1)pi//2 , n in Z (c) neither continuous nor differentiable at (2n+1)pi//2 , n in Z (d) none of these

Let f(x)={1, x =1 . Then, f is (a) continuous at x=-1 (b) differentiable at x=-1 (c) everywhere continuous (d) everywhere differentiable

If f(x)={1/(1+e^(1//x)),\ \ \ \ x!=0 0,\ \ \ \ \ \ \ \ \ \ \ x=0 , then f(x) is continuous as well as differentiable at x=0 (b) continuous but not differentiable at x=0 (c) differentiable but not continuous at x=0 (d) none of these

The function f : R rarr R given by f(x) = - |x-1| is (a) continuous as well as differentiable at x = 1 (b) not continuous but differentiable at x = 1 (c) continous but not differentiable at x = 1 (d) neither continous nor differentiable at x = 1

The function f(x)=sin^(-1)(cosx) is discontinuous at x=0 (b) continuous at x=0 (c) differentiable at x=0 (d) none of these