Differentiation Question 164
Question: $ \underset{x\to \pi /2}{\mathop{\lim }}\frac{[ \frac{x}{2} ]}{ln(sinx)} $ (where [.] denotes the greatest integer function)
Options:
A) Does not exist
B) Equals 1
C) Equals 0
D) Equals -1
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ \because \frac{\pi }{4}<1,\therefore [ \frac{\pi }{4} ]=0\therefore \underset{x\to \pi /2}{\mathop{\lim }}\frac{[ \frac{x}{2} ]}{In(sinx)}=0. $
BETA
