" Ef Show that the function "f(x)={[(x)/(|x|),," when "x!=0],[1,," when "x=0]

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.

Show that the function f(x) ={( (sin x)/x, when x !=0),( 2, when x =0):} is continuous at each point except 0.

Show that the function f(x)={x sin((1)/(x)) when x!=0;=0, when x=0 is continuous butnot differentiable 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

Show that the function f(x)={x(sin1)/(x)quad ,quad when x!=00quad when x=0 is continuous but not differentiable at x=0 .

Show that the function f(x)={ x^2sin(1/x) , when x !=0 and 0 when x=0 } is differentiable at x=0.

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

Examine the continuity of the function f(x)={{:((|"sin"x|)/(x),"when " xne0),(" 1","when "x=0):}