jee-main 2019 Q74

jee-main · India · session1_09jan_shift2 Sign Change & Interval Methods
For each $x \in R$, let $[x]$ be the greatest integer less than or equal to $x$. Then $\lim_{x \rightarrow 0^-} \frac{x([x] + |x|)\sin[x]}{|x|}$ is equal to
(1) 1
(2) 0
(3) $-\sin 1$
(4) $\sin 1$
For each $x \in R$, let $[x]$ be the greatest integer less than or equal to $x$. Then $\lim_{x \rightarrow 0^-} \frac{x([x] + |x|)\sin[x]}{|x|}$ is equal to\\
(1) 1\\
(2) 0\\
(3) $-\sin 1$\\
(4) $\sin 1$