If the function `f(x) ={{:((sinx)/(kx)+k",when "xne0),(2" when "x=0):}` is continuous at x = 0, find k.

If the function f(x)={{:((1-cos(ax))/(x^2)," when "xne0),(1," when "x=0):} be continuous at x=0, then find the value of a.

Show that the function f(x)={{:(x"cos"(1)/(x),"when"xne0),(0,"when"x=0):} is continuous at x=0.

If the function f(x) = {((sin x)/(kx)+k, x!=0),(2,x=0):} is continuous at x= 0 , find k.

Show that the function f(x)={{:(x+(x+2)/(|x+2|),"when " xne-2),(" "-1,"when " x=-2):} is dicontinuous at x=-2 Also find the jump of f (x) at this point of discontinuity.

Find the value of k for which the function f(x)={{:(kx+2 ,"when " xlepi),(cosx," when " xgtpi):} , is continuous at x=pi .

If f(x) = (sin 5x)/(2x) (when x!=0 ) = (5k)/4 (when x= 0), and f(x) is continuous at x=0, find k.

Let [x] denote the greatest integer less than or equal to x Then the value of a for which the function f(x)={((sin[-x^(2)])/([-x^(2)])",",xne0),(alpha",",x=0):} is continuous at x=0 is

Find the value of k for which the function f(x)={{:(kx+4,"when " xlepi),(cosx," when " xgtpi):} , is continuous at x=pi .

If f(x)={((sin5x)/(x^(2)+2x),"when "x ne 0),(k+(1)/(2),"when "x =0):} is continuous at x=0, then the value of k is-

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