Discuss the continuity of the following function : `f(x)={1,ifxi sr a t ion a l0,ifxi si r r a t ion a l`

Discuss the continuity of the function f(x) = |x -1| at x=1

Discuss the continuity of the function defined by f(x)={x+2, if x 0

Discuss the continuity of the function f (x)= |x| " at " x=0

Discuss the continuity of the function f defined by f(x)=1/x , x!=0 .

Discuss the continuity of the function f given by f(x) = |x| a t x = 0 .

Column I: Function, Column II: Type of function f(x)="{"sgnx")"^(sgn)}; x!=0,n is an odd integer, p. odd function f(x)=x/(e^x-1)+x/2+1 , q. even function f(x)={0,ifxi sr a t ion a l1,ifxi si r r a t ion a l , r. neither odd nor even function. f(x)=max{tanx ,cotx} , s. periodic

Find the value of x where f(x)={x ,ifxi sr a t ion a l1-x ,ifxi si r r a t ion a li scon t inuou sdot

Discuss the continuity of the function f(x)={((|x|)/x", " xne 0),(1", " x=0):} at x=0

Discuss the continuity of the function f(x) ={:{((Sinx)/(x) ", "x lt0 ),(x+1 ", " x ge0):}, at =0.

Differentiate the following functions w.r.t. x. f(x) = sqrt( x^2 +1)