The function f (x) is continuous at x = 0 of -

Let f(x+y) = f(x) + f(y) for all x and y. If the function f (x) is continuous at x = 0 , then show that f (x) is continuous at all x.

Consider the following for the next two items that follows f(x)={{:(x+pi" for "x in[-pi,0)),(picosx" for "x in[0,(pi)/(2)]),((x-(pi)/(2))^(2)" for "x in((pi)/(2),pi]):} Consider the following statement: 1. The function f(x) is continuous at x = 0. 2. The function f(x) is continuous at x=(pi)/(2) Which of the above statements is / are correct?

If the following function f (x) is continuous at x = 0 , find k : f(x)={{:((1-cos2mx)/(2x^(2)),"when " xne0),(" " k,"when " x =0):}

If f(x)={alpha+sin[x]/x , x > 0 and 2 ,x=0 and beta+[(sin x-x)/x^3] ,x < 0 (whlenotes the greatest integer function) if f(x) is continuous at x = 0 . then beta is equal to

If f(x)=[(3sin x)/(x)],x!=0, then the value of f(0) so that the function f(x) is continuous at x=0 is

If the following function f(x) is continuous at x = 0, find the value of 'a': f(x) = {:{((1-cos4x)/x2,x 0):}

Let f(x+y)=f(x)+f(y) for all x and y If the function f(x) is continuous at x=0 show that f(x) is continuous for all x

Let f(x+y)=f(x)+f(y) for all xa n dydot If the function f(x) is continuous at x=0, show that f(x) is continuous for all xdot

Let f(x+y)=f(x)+f(y) for all xa n dydot If the function f(x) is continuous at x=0, show that f(x) is continuous for all xdot

Let f(x+y)=f(x)+f(y) for all xa n dydot If the function f(x) is continuous at x=0, show that f(x) is continuous for all xdot