Direction (Q. Nos. 87) For the existence of limit at \[x=a\] of \[y=f(x)\] it must be true that\[\underset{x\to \infty }{\mathop{\lim }}\,\,f(a+h)=\underset{h\to 0}{\mathop{\lim }}\,f(a+h)\]. Here, \[x=a\] is not the end point of the interval, \[\underset{x\to 0}{\mathop{\lim }}\,f(a-h)\] is called LHL and \[\underset{x\to 0}{\mathop{\lim }}\,f(a+h)\] is called RHL. |
A) 0
B) Does not exist
C) - 1
D) 1
Correct Answer: A
Solution :
\[RHL=\underset{h\to 0}{\mathop{\lim }}\,\,\left[ \sin \,\left( \frac{\pi }{2}+h \right) \right]=0\] \[LHL=\,\underset{h\to 0}{\mathop{\lim }}\,\,\left[ \sin \,\left( \frac{\pi }{2}-h \right) \right]=0\]You need to login to perform this action.
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