If `f(x)={{:(x+sinx,"when "xlt0),(0,"when "xge0):}`
examine whether f(x) is continuous at x = 0.

A function f (x) is defined as followes: f(x)={{:(xsin.(1)/(x),"when " xne0),(0,"when " x=0):} Show that f (x) is continuous at x =0 .

f(x)={{:(" "2,"when "xlt0),(2+sinx,"when "xge0):} Show that f (x) is continuous at x = 0 but f ' (0) does not exist.

A function f (x) is defined as follows: f(x)={{:(x+2,"when "xlt2),(x^(2)-1,"when "xge2):} Show that f (x) is discontinuous at x = 2 and the jump of the function at this point is -1 .

The function f (x) is continuous at x = 0 of -

Sketch the graph of the function : f(x)=0," when "x lt1 =x-1," when "x ge1 From the graph examine whether f(x) is continuous at x =1 or not.

Draw the graph of the function : f(x)=1+2x," when "xle1 =3-x," when "x gt1 From the graph examine whether f(x) is continuous at x = 1 or not.

Given , f(x)={{:((1-cos3x)/(x^(2)),"when " xne0),(1,"when "x=0):} Prove that f (x) is discontinuous at x = 0 .

If f(x)={{:((|sinx|)/(x),"when "xne0),(1,"when "x=0):} then examine the continuity of the function at x = 0.

Given , f(x)={{:((sin5x)/(3x),"when "xne0),((3)/(5),"when "x=0):} Examine the cotinuity of f (x) at x = 0 .

If the function f(x) ={{:((sinx)/(kx)+k",when "xne0),(2" when "x=0):} is continuous at x = 0, find k.