Type of Discontinuity - removable or irremovable

Types OF discontinuity

Single point continuity , Type OF discontinuity( Removable & Non Removable) ,Differentiability based questions

Discuss the conjinuity 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)=log(100(0.01+x))/(3x), {:("for"x ne0),(",""for"x=0):}}at=0. =100/3

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 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)=xsin(1/x)" , for "x ne0),(=0" , for "x=0):}} at x=0

If f(x)={sin((a-x)/(2))tan[(pi x)/(2a)] for x>a and ([cos((pi x)/(2a))])/(a-x) for x

If the function f(x)=(1)/(In|x|) has irremovable discontinuity at x=a&b and removable discontinuityat x=c, then find a^(2)+b^(2)+c^(2)

Consider the function defined on [0,1] -> R, f(x) = (sinx - x cosx)/x^2 and f(0) = 0, then the function f(x)-(A) has a removable discontinuity at x = 0(B) has a non removable finite discontinuity at x = 0(C) has a non removable infinite discontinuity at x = 0(D) is continuous at x = 0

The points of discontinuity of tan x are

If f(x)={(2cos x-sin2x)/((pi-2x)^(2)),x (pi)/(2) then which of the following holds? (a)f is continuous at x=pi/2( b) f has an irremovable discontinuity at x=pi/2( d) f has a removable discontinuity at x=pi/2( d) None of these