[" Examine the continuity of "],[qquad [f(x),=(1+2x)^(1/x)," for "x!=0],[,=e^(2)," for "x=0]}" at "x=0]

Examine the continuity of a function f(x)={{:(|x|"cos"(1)/(x)", if "x!=0),(0", if "x=0):} at x=0 .

Examine the continuity of f(x) at x=0 if f(x)= (sin 2x)/(2x), x ne 0

Examine the continuity of f(x) = {{:((x)/(|x| )"," ,"if " x != 0),(0",", "if "x = 0):} at x = 0

Examine the continuity of f(x)= sin (pi(x))/2 at x = 0.

Examine the continuity of the following function f(x)={{:((x)/(2|x|)", "x!=0),((1)/(2)", "x=0):} at x=0.

Examine the continuity of the function f(x)={{:((|sinx|)/(x)", "x!=0),(1", "x=0):} at x=0

Examine the continuity of f(x) = {((sinx)/x,x ne 0),(1,x = 0):} at x =0

Examine the continuity of the function f(x)= {((1-cos(2x))/(x^(2)),"if "x ne 0),(5",","if" x = 0):} at x=0

Examine the continuity of the function f (x)={((1)/(x+[x]),ifx<0),(-1,if xge0):} at x=0.