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 .

Find real contans, a b so that the function 'f' given by f(x)={{:(sinx , if, x le0),(x^(2)+a, if, 0 lt x lt 1),(bx+3,if, 1 le x le 3),(-3,if,x gt 3):} is continuous on R.

Find the value of 'a' so that Find the values of a and b so that the function defined by f (x) = {{:(ax^(2) + 9x - 5 " if " x lt 1 ), (b " if " x = 1 ),((x + 3) (2x -9) " if " x gt 1 ):} is continuous on R .

Is the function f , defined by f(x)={{:(x^(2),"if "xle1),(x,"if "xgt1):} continuous on R ?

Find the relationship between a and b so that the function f defined by f(x)={{:(ax+1," if "x le 3),(bx+3," if "x gt 3):} is continuous at x=3.

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.

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.

Check the continuity of the function f given by f(x)= 2x+3" at "x=1 .

Discuss the continuity of the function f given by f(x)= x^(3)+x^(2)-1 .