Continuity of a Function at a Point

Define continuity and differentiability of a function at a point verify the continuity and differentiability of the function: , f(x)={[(1-x),x 2])

Discuss the continuity of the functions at the points shown against them . If a function is discontinuous , determine whether the discontinuity is removable . In this case , redefine the function , so that it becomes continuous : {:(F(x)=(4^(x)-e^(x))/(6^(x)-1)" , for "x ne0),(=log((2)/(3))" , for "x =0):}} at x =0 .

Discuss the continuity of the functions at the points given against them. If a function is discontinuous, determine whether the discontiunity is removable. In this case, redefine the function, so that it becomes continuous : {:(f(x)=(1+cos 2x)^(4sec2x)",","for"x nepi/4),(=e^(4)",","for" x=pi/4):}}at x=pi/4*

Discuss the continuity of the functions at the points given against them. If a function is discontinuous, determine whether the discontiunity is removable. In this case, redefine the function, so that it becomes continuous : {:(f(x)=(logx-log7)/(x-7)",","for" x ne7),(=7",","for" x=7):}}at x=7.

Discuss the continuity of the functions at the points given against them. If a function is discontinuous, determine whether the discontiunity is removable. In this case, redefine the function, so that it becomes continuous : {:(f(x)=((3^(sinx)-1)^(2))/(x log(1+x))",","for" x ne0),(=2log3",", "for" x=0):}}at x=0.

Discuss the continuity of the functions at the points given against them. If a function is discontinuous, determine whether the discontiunity is removable. In this case, redefine the function, so that it becomes continuous : {:(f(x)sin x-cosx",", "for"x ne0),(=-1",","for"x=0):}}at x=0.

Discuss the continuity of the functions at the points given against them. If a function is discontinuous, determine whether the discontiunity is removable. In this case, redefine the function, so that it becomes continuous : {:(f(x)=(e^(5x)-e^(2x))/(sin3x)",", "for" x ne0),(=1",", "for" x=0):}}at x=0.

Discuss the continuity of the functions at the points given against them. If a function is discontinuous, determine whether the discontiunity is removable. In this case, redefine the function, so that it becomes continuous : {:(f(x)=(x^(2)-4x)/(sqrt(x^(2)+9)-5)",","for" x ne4),(=3",", "for"x=4):}}at x =4.

Discuss the continuity of the functions at the points given against them. If a function is discontinuous, determine whether the discontiunity is removable. In this case, redefine the function, so that it becomes continuous : {:(f(x) =(log(2+x)-log(2-x))/(tanx)",","for" xne0),(=1",","for" x=0):}}at x=0.