Show that `f (x) = ((x+1",", if x le 2),( x^(2)+1)",", if x lt 1):}` is continuous at x =1

show that f(x) ={{:( (2x-1)",",if , x lt2),( (3x)/2",,if x ge 2):} is continuous

If f(x) {:(=px-q", if " x le 1 ),(= 3x ", if " 1 lt x lt 2 ), (= qx^(2)-p ", if " x ge 2 ):} is continuous at x = 1 and dicontinuous at x = 2 , then

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 .

Show that f(x)={{:(x^(2),if, 0 le x le 1),(x ,if, 1 le x le 2):} is continuous on [0,2]

If f(x) {:(=3k", if "x le 1/2 ),(= 3/2-2x " , if " 1/2 lt x lt 1 ):} is continuous at x = 1/2 , " then " k = …….

If f(x)= {{:((sqrt(1+lambdax)- sqrt(1 - lambdax))/(x) "," -1 le x lt 0 ),((2x + 1)/(x - 2) ", " - 0le x lt 1):} is continuous at x = 0 then lambda = ?

If the function f(x) ={(ax-b, x le1),(3x, 1lt x lt 2),(bx^(2)-a, x ge 2):} is continuous at x =1 and discontinuous at x =2, then

Show that the function f(x)={:{(1-x", " x lt1),(x^2-1 ", " x ge 1):} is continuous but not differnetiable at x=1

Show that the function f(x)={:{(1-x", " x lt1),(x^2-1 ", " x ge 1):} is continuous but not differnetiable at x=1

If f(x) {:(=x^(2)-1", if "x lt 3 ),(= 2ax ", if "x le 3 ) :} is continuous at x = 3 , then a = ……