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

If a function f(x) is defined by f(x) = {((1+7x)^(1/x),when x!=0),(k,when x =0):} is continuous at x = 0, then what is the value of k.?

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

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.

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

If f(x)=(e^((1)/(x))-1)/(1+e^((1)/(x))) when x!=0=0, when x=0 show that f(x) is discontinuous 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)={{:(x"cos"(1)/(x),"when"xne0),(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.