If `f(x)={(ax^2+b if x lt1),(1 if x=1),(2ax-b if xgt1):}`
is continuous at x=1, then find a and b.

If the function f(x)={:{(3ax+b", if "xgt1),(11", if "x=1),(5ax-2b", if "xlt1):} is continuous at x=1 , then find the values of a and b

If the function f(x) defined by f(x)={((log(1+ax)-log(1-bx))/(k)", if "x!=0),(" k, if "x=0):} is continuous at x=0 , then find the value of k.

Is the function f defined by f(x)={(x", if "xle1),(5", if "xgt1):} continuous at x=0, at x=1 and at x=2 ?

Find the relationship between a and b so that the function f defined by f(x)={(ax+1" , if "xle3),(bx+3" , if "xgt3):} is contunuous at x=3.

For what value of lamda is the function f(x)={{:(lamda(x^(2)-2x)", if "xle0),(4x+1", if "xgt0):} continuous at x=0 ? What about continuity at x=1 ?

Find the value of k for which f(x)={{:((sqrt(1+kx)-sqrt(1-kx))/(x)", if "-1lexlt0),(" "(2x+1)/(x-1)", if "0lexlt1):} is continuous at x = 0

Find the relationship between a and b so that thefunction defined by f(x)={(ax+b,if,xle3),(bx+3, if, x>3):} s continuous at x = 3.

Find the values of a and b such that the function f defined by f(x)={:{((x-4)/(|x-4|)+a", if "xlt4),(a+b", if "x=4" is a"),((x-4)/(|x-4|)+b", if "xgt4):} continuous function at x=4 .

Show that f(x) = {:{(5x-4, when, 0 lt x le 1), (4x^(2) - 3x, when, 1 lt x lt 2):} is continuous at x = 1 .