Examine the contionuity of the following functions at the give points `f(x)={(log100+log(0. 01+x))/(3x)` for `x!=0` and `100/3` for x =0 } at `x=0`

Examine the continuity of the following functions at indicated points. f(x)={(frac{[x]}{x}ifxne0 at x=0),(0 if x=0):}

If f(x) is continuous at x=0 , where f(x)=(log 100 + log (0.01 +x))/(3x) , for x!=0 , then f(0)=

Examine the continuity of the function f(x) = {:{(3x-2,xle0),(x+1,x>0):} at x = 0

if the function f(x) defined by f(x)=(log(1+ax)-log(1-bx))/(x), if x!=0 and k if x=0 is continuous at x=0, find k

If the function f(x) defined by f(x)=(log(1+3x)-log(1-2x))/(x),x!=0 and k

If the function f(x) defined by f(x)= (log(1+3x)-"log"(1-2x))/x , x!=0 and k , x=0. Find k.

if the function f(x) defined by f(x)= (log(1+a x)-"log"(1-b x))/x , if x!=0 and k if x=0 is continuous at x=0 , find k.

In (0, infty) then function f(x)=(log (1+x))/(x) is

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