A) Is continuous at \[x=0\]
B) Has removable discontinuity at \[x=0\]
C) Has jump discontinuity at \[x=0\]
D) Has oscillating discontinuity at \[x=0\]
Correct Answer: D
Solution :
[d] We have \[\underset{x\to {{0}^{-}}}{\mathop{\lim }}\,f(x)=\underset{h\to 0}{\mathop{\lim }}\,\sin ({{\log }_{e}}\left| -h \right|)\] \[=\underset{h\to 0}{\mathop{\lim }}\,\sin ({{\log }_{e}}h)\] Which does not exist but lies between -1 and 1. Similarly, \[\underset{x\to {{0}^{+}}}{\mathop{\lim }}\,f(x)\] lies between -1 and 1 but cannot be determined.
You need to login to perform this action.
You will be redirected in
3 sec
