If `f(x)={[1/(x^2)-1/(x^2),xlt0],[sin^(-1)(x+b),x gt-0]}` then at `x=0,f(x)` is
(a)continuous if `b=0`
(b)discontinuous for any real `b`
(c)differentiable for `b=+-1`
(d)non-differentiable for any real `b`

The function f(x)=1+|cosx| is (a) continuous no where (b) continuous everywhere (c) not differentiable at x=0 (d) not differentiable at x=npi,\ \ n in Z

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 discontinuous at x=0 (b) continuous at x=0 (c) differentiable at x=0 (d) none of these

If f(x)=x^2+(x^2)/(1+x^2)+(x^2)/((1+x^2)^2)+. . . . +(x^2)/((1+x^2)^n)+ , then at x=0,f(x) (a)has no limit (b) is discontinuous (c)is continuous but not differentiable (d) is differentiable

If f(x)=sum_(n=0)^oo x^n/(n!)(loga)^n , then at x = 0, f(x) (a) has no limit (b) is discontinuous (c) is continuous but not differentiable (d) is 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)={(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/(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

Let f(x) ={{:( xe^(x), xle0),( x+x^(2)-x^(3), xgt0):} then the correct statement is (a) f is continuous and differentiable for all x (b) f is continuous but not differentiable at x=0 (c) f is continuous and differentiable for all x . (d) f ' is continuous but not differentiable at x=0

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