At `x=3, f(x) ={(x^(5)-243",", "if " x ne 3),(x^(3)-27",", "if " x=3):}` is

f(x)=x^(3)+27x+5

If the function f(x)={{:((x ^(2) -9)/(x-3), "when" x ne3),(2x+a, "when" x=3):} is such that lim _(x to3) f(x) =f(3), then the value of a is-

Examine the following functions for continuity: f(x) = {:{((|x-3|)/(2(x-3)), if x ne 3),(0, if x =3):} at x = 3

If f(x)={{:((log x-log3)/(x-3),"for "x ne 3),(c,"for "x =3):} is continuous at x = 3, then the value of c is

For the function f(x)={((x^(3)-a^(3))/(x-a)",",x ne a),(b" ,",x =a):} , if f(x) is continuous at x = a, then b is equal to

For the function f(x)={((x^(3)-a^(3))/(x-a)",",x ne a),(b" ,",x =a):} , if f(x) is continuous at x = a, then b is equal to

f(x) = {{:(((27- 2x )^(1//3)-3)/(9-3 (243 + 5x)^(1//5)) " if " x ne 0),(k " if " x = 0 ):} continuous at x = 0 then k =

Evaluate right-handed limit of the function : f(x)={{:(abs(x-3)/(x-3)",",x ne 3), (" 0,", x=3):} at x = 3.