Question

$\underset{x\to 0}{\lim }\left[\min \left(y^2-4y+11\right)\frac{\sin x}{x}\right]$ (where $[\cdot ]$ denotes the greatest integer function) is

• A. 5
• B. 6
• C. 7
• D. does not exist

Answer 1

Answer: (B)

$\min \left(y^2-4y+11\right)=\min \left[(y-2{)}^2+7\right]=7$
or $L=\underset{x\to 0}{\lim }\left[\min \left(y^2-4y+11\right)\frac{\sin x}{x}\right]$
$=\underset{x\to 0}{\lim }\left[\frac{7\sin x}{x}\right]$
$=[$ a value slightly lesser than 7$]=6.$
$(|\sin x|<|x|$, when $x\to 0)$