Differentiation Question 121
Question: $ \underset{x\to 0}{\mathop{\lim }}\frac{\sin [cosx]}{1+[cosx]} $ ( $ [\cdot ] $ denotes the greatest integer function)
Options:
A) Equal to 1
B) Equal to 0
C) Does not exist
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
L.H.L $ =\underset{x\to 0-}{\mathop{\lim }}f(x)=\underset{h\to 0}{\mathop{\lim }}\frac{\sin [h]}{1+[h]}=\frac{\sin (0)}{1+0}=0 $
$ (\therefore h>0\Rightarrow \cosh<1) $ R.H.L. $ =\underset{x\to 0+}{\mathop{\lim }}f(x)=\underset{h\to 0}{\mathop{\lim }}\frac{\sin [\cosh]}{1+[\cosh]}=\frac{\sin (0)}{1+0}=0 $
BETA
