" 6."f(x)={[(1-cos x)/(x^(2)),," when "x times0;" is discontinuous at "x=0],[1,," when "x=0]

Let f(x)={(1-cos x)/(x^(2)), when x!=01,quad when x=0. Show 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)={sin((1)/(x)),x!=00,x=0 then it is discontinuous at-

f(x)={{:(3-x",","when",x le0, ),( x^(2)",", "when",xgt0):} is discontinuous at x=0

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

Show that f(x)={(x-|x|)/(2),quad when x!=02,quad when x=0 is discontinuous at x=0 .

Show that the function f(x) given by f(x)={((e^(1/x)-1)/(e^(1/x)+1), when x!=0), (0, when x=0):} is discontinuous at x=0 .

Show that the function f(x) given by f(x)={(e^(1/x)-1)/(e^(1/x)+1), when x!=00,quad when x=0 is discontinuous at x=0

Is f(x)=(1+x)^((1)/(x)), when x!=0=e, when x=0 continuous at x=0?

f(x)={{:((sin3x)/(x)",","when",x ne0 ),( 1",", "when",x=0):} is discontinuous atx =0.