Let `f(x)={{:((1-cos2ax)/(xsin2x),"when " xne0),(" " (1)/(2),"when " x =0):}` If f (x) is continuous at x = 0 , find the value of `alpha` .

Given , f(x)={{:((1-cos3x)/(x^(2)),"when " xne0),(1,"when "x=0):} Prove that f (x) is discontinuous at x = 0 .

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.

If f(x)={{:((1-cosKx)/(x sin x)",","if "xne0),((1)/(2)",","if "x=0):} is continuous at x=0 , then the value of

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

(i) Given f(x)={((1-cos4x)/(x^(2))" , "xne0),(k" , "x=0):} If f(x) is continuous at x=0, find the value of k. (ii) Given f(x)={((1-cos4x)/(8x^(2))" , "xne0),(k" , "x=0):} If f(x) is continuous at x=0, find the value of k.

If f(x) = {((1-cos4x)/x^2, when x 0):} . is continuous at x=0, then the value of a will be.

Let f(x)={{:((1)/(x^(2))sin(x^(2))," when "xne0),(0," when " x=0):} Discuss the continuity of f (x) at x = 0 .

If f(x)={{:("x sin"(1)/(x)",",xne0),(k",",x=0):} is continuous at x=0, then the value of k is

If f(x)={{:((|sinx|)/(x),"when "xne0),(1,"when "x=0):} then examine the continuity of the function at x = 0.

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