Is the function defined by `f(x)={{:(x, ifxle1),(5, ifx >1):}` a continuous function at `x=0,x=1`and `x=2`

Is the function f defined by f(x)={{:(x, if x le 1),(5, if x gt 1):} continuous at x = 0? At x = 2 ?

Is the function defined by f(x)={x+5, if x 1 a continuous function?

Is the function f defined by f(x)={x , if""""xlt=1 5, if""""x >1 continuous at x" "=" "0?" "A t" "x" "=" "1?" "A t" "x" "=" "2?

If the function defined by : f(x)={{:(2x-1", "xlt2),(a", "x=2),(x+1", "xgt2):} is continuous at x = 2, find the value of 'a'. Also discuss the continuity of f(x) at x = 3.

Function f(x)={(x-1",",x lt 2),(2x-3",", x ge 2):} is a continuous function

Show that the function defined by f(x)=cos(x^(2)) is a continuous function.

Show that the function defined by f(x)=sin(x^(2)) is a continuous function.

If the function defined by f(x) = {((sin3x)/(2x),; x!=0), (k+1,;x=0):} is continuous at x = 0, then k is

Find the value of a' for which the function f defined by f(x)={a(sin pi)/(2)(x+1),quad x 0 is continuous at x=0