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 1.0
C) Equals 0
D) Equals -1
Show Answer
Answer:
Correct Answer: C
Solution:
$ \because \frac{\pi }{4}<1,\therefore \left\lfloor \frac{\pi }{4} \right\rfloor=0\therefore \underset{x\to \pi /2}{\mathop{\lim }}\frac{\left\lfloor \frac{x}{2} \right\rfloor}{\ln(\sin x)}=0. $
BETA
