[" 21.The function "f(x)={[(|x|)/(x),," when "],[0,," when "],[" has discontinuity at "x=0," of the kind: "]]

The function f(x)={[(|x|)/(x) , if x!=0],[0, if x=0 is discontinuous at

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

Show that f(x)={(|x-a|)/(x-a),quad when x!=a1,quad when x=a is discontinuous at x=a

Show that the function f(x)={{:(x/|x|",", " when ", x ne0),(1",", " when ", x =0):} is discontinuous at x=0

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

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

If the function f(x) = {((sin^(2)ax)/(x^(2))","," when "x != 0),(" k,"," when " x = 0):} is continuous at x = 0 then k = ?

Show that the function 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 funcation f(x)={{:(3x-2",", " when ", x le0),(x+1",", " when ", x gt 0):} is discontinuous at x =0