MCQ
Let $[ t ]$ denote the greatest integer $\leq t$. If for some $\lambda \in R -\{0,1\}, \lim \limits_{x \rightarrow 0}\left|\frac{1-x+|x|}{\lambda-x+[x]}\right|=L,$ then $L$ is equal to
- A$1$
- ✓$2$
- C$\frac{1}{2}$
- D$0$
$\operatorname{RHL}: \lim _{x \rightarrow 0^{+}}\left|\frac{1-x+x}{\lambda-x+1}\right|=\left|\frac{1}{\lambda}\right|$
For existence of limitt
$LHL = RHD$
$\Rightarrow \frac{1}{|\lambda-1|}=\frac{1}{|\lambda|} \Rightarrow \lambda=\frac{1}{2}$
$\therefore \quad L=\frac{1}{|\lambda|}=2$
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