" 3.Show that the function "f(x)={[(x^(n)-1)/(x-1),," when "x!=1;],[n,," when "x=1]" is continuous."

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)= {{:(( x^(n) -1)/(x-1)",", "when", x ne 1),( n "," , "when", x =1):} is continuous.

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

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

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 .

If the function f(x)={{:((x^(2)-1)/(x-1), "When ", x ne1),(k, "When" , x=1):} is given to be continuous at x=1, then the value of k is ____.

If the function f(x)={{:((x^(2)-1)/(x-1), "When ", x ne1),(k, "When" , x=1):} is given to be continuous at x=1 , then the value of k is ____.

If the function f(x)={{:((x^(2)-1)/(x-1), "When ", x ne1),(k, "When" , x=1):} is given to be continuous at x=1, then the value of k is ____.