x 0 12. The jump of f(x) x 1, x -0 b) -1 a) 0 13. At 0, the function f(x) X x is a) continuous only c) 2 b) discontinuous

Show that the function f(x) = x cos (1//x), x ne 0 f(0) = 1 is discontinuous at x = 0.

if f(x)=x^2sin(1/x) , x!=0 then the value of the function f at x=0 so that the function is continuous at x=0

if f(x)=x^2sin(1/x) , x!=0 then the value of the function f at x=0 so that the function is continuous at x=0

A function is defined as f(x) = {{:(e^(x)",",x le 0),(|x-1|",",x gt 0):} , then f(x) is(a) continuous at x = 0 ,(b) continuous at x = 1 (c)differentiable at x = 0

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

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

Show that the function f(x)=(x)/(1+e^(1//x),x ne 0, f(0)= 0 is continuous at x = 0

1.If lim_(x rarr0)(f(x))/(x) exists and f(0)=0 then f(x) is (a) continuous at x=0 (b) discontinuous at x=0 (e) continuous no where (d) None of these

Let [.] denotes G.LP. for the function f(x)=(tan (pi[x-pi])/(1+[x]^2)) the wrong statement is (A) f(x) is discontinuous at x=0 (B) f(x) is continuous for all values of x (C) f(x) is continuous at x=0 (D) f(x) is a constant function

if f(x) ={{:( (x log cos x)/( log( 1+x^(2) )), x ne 0) ,( 0, x=0):} a. f is continuous at x = 0 b. f is continuous at x = 0 but not differentiable at x = 0 c. f is differentiable at x = 0 d. f is not continuous at x = 0