Is f given by `f(x)={{:((x^2-9)/(x^2-2x-3)" if "0ltxlt5 " and "xne3),(1.5" "" if "x=3):}`, continuous at the point 3.

Is f given by f(x)={{:((x^(2)-9)/(x^(2)-2x-3),"if "0ltxlt5andxne3),(1.5,"if "x=3):} , continuous at the points 3 .

Check the continuity of the functionn 'f' defined by fx={{:((x^(2)-9)/(x^(2)-2x-3),if, 0 lt x lt 5 and x ne3),(1.5,if,x=3):}

Find the real constants a , b, so that the function f given by f(x)={{:(sinx,"if "xle0),(x^(2)+a,"if "0ltxlt1),(bx+3,"if "1lexle3),(-3,"if "x gt3):} is continuous on R .

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 =

Show that the function f given by f(x)= {{:(x^3+3," if "x ne 0),(1," if "x=0):} is not continuous at x=0.

Show that f(x)={{:((cosax-cosbx)/(x^(2))," if " xne0),((1)/(2)(b^(2)-a^(2))," if "x=0):}"is continuous at 0"

Is f defined by f(x)={{:((sin2x)/(x),"if "xne0),(1,"if "x=0):}" continuous"0 ?