Differentiation Question 109
Question: $ \underset{x\to 0}{\mathop{\lim }}[ \min (y^{2}-4y+11)\frac{\sin x}{x} ] $ (where [.] denotes the greatest integer function) is
Options:
A) 5
B) 6
C) 7
D) Does not exist
Show Answer
Answer:
Correct Answer: B
Solution:
[b] min $ (y^{2}-4y+11)=min[{{(y-2)}^{2}}+7]=7 $ or $ L=\underset{x\to 0}{\mathop{\lim }}[ \min (y^{2}-4y+11)\frac{\sin x}{x} ] $
$ =\underset{x\to 0}{\mathop{\lim }}[ \frac{7\sin x}{x} ] $ = [a value slightly lesser than 7] $ (| \sin x |<| x |,whenx\to 0) $
$ =\underset{x\to 0}{\mathop{\lim }}[ 7\frac{\sin x}{x} ]=6. $
BETA
