Question

$\underset{x\to \frac{-1}{3}}{lim}\frac{1}{x}\left[\frac{-1}{x}\right][.]\to denotesgreatestintegerfunction$

• A. -9
• B. -12
• C. - 6

Answer 1

The correct option is C - 6

$x<-\frac{1}{3}\frac{1}{x}>-3\Rightarrow -\frac{1}{x}<3\Rightarrow [-\frac{1}{3}]=2\underset{x\to -\frac{1}{3}}{lim}\frac{1}{x}[-\frac{1}{x}]=(-3)\left(2\right)=-6$