Consider the function g/defined by `g(x) = {x^2 sin(pi/x) +(x-1)^2sin(pi/(x-1)),x!=0,1; 0, if x=0,1}` then which of the following statement(s) is/are correct? (A) g (x) is differentiable `AA in R`. (B) g(x) is discontinuous at x=0 but continuous at x = 1 . C) g(x) is discontinuous at both x =0 and x = 1 D) Rolle's theorem is applicable for g(x) in [0, 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

The function f(x)=sin^(-1)(cosx) is (a) . discontinuous at x=0 (b). continuous at x=0 (c) . differentiable at x=0 (d) . non of these

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

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

Let f(x)=[x], where [.] is the greatest integer fraction and g(x)=sin x be two valued functions over R. Which of the following statements is correct? (a) Both f(x) and g(x) are continuous at x=0 (b) f(x) is continuous at x=0, but g(x) is not continuous at x=0. (c) g(x) is continuous at x=0, but f(x) is not continuous at x=0. (d) Both f(x) and g(x) are discontinuous at x=0

Statement I f(x) = sin x + [x] is discontinuous at x = 0. Statement II If g(x) is continuous and f(x) is discontinuous, then g(x) + f(x) will necessarily be discontinuous at x = a.

Statement I f(x) = sin x + [x] is discontinuous at x = 0. Statement II If g(x) is continuous and f(x) is discontinuous, then g(x) + f(x) will necessarily be discontinuous at x = a.

Statement I f(x) = sin x + [x] is discontinuous at x = 0. Statement II If g(x) is continuous and f(x) is discontinuous, then g(x) + f(x) will necessarily be discontinuous at x = a.

Consider the following for the following: Let f(x)={-2, -3<=x<=0; x-2, 0

If g(x)=int_0^x2|t|dt ,then (a) g(x)=x|x| (b) g(x) is monotonic (c) g(x) is differentiable at x=0 (d) gprime(x) is differentiable at x=0