f(x)={[(|x-3|)/(x-3),,x!=3],[0,,x=3]

Let f(x)={[((e^(3x)-1))/(x),,x!=0],[3,,x=0]} then 2f'(0) is

Let f(x)={{:((|x-3|)/((x-3))",",xne3),(0",",x=3.):} Show that lim_(xrarr3)f(x) does not exist.

Verify the existence of lim_(x to 3) f(x) , where f(x)={:{(|x-3|/(x-3),for , xne 3),(0, for ,x =3):}

Suppose that f(x)=x^(3)-3x^(2) and h(x)=[(f(x))/(x-3),x!=3 then K,x=3

Test the continuity of the function at x = 3 , where f(x) = {{:((|x-3|)/(x(x - 3))"," ,x != 3),(0",", x = 3):}

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

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

(i) Dissusse the continuity of the function f(x)={(|x-a|", " xne a ),(" "0 ", "x=a):} at x=a (ii) Discuss the continutiy of the function f(x)={(|x-3|/(x-3)", " xne 3 ),(" "0 ", "x=3):} at x=3

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