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

JEE Main · 2019 · 09 Jan 2019 · Shift 2 · Limits

For each

x \in R

, let

[x]

be the greatest integer less than or equal to

x

. Then

lim_{x \to 0^{+}} \frac{x ([ x ] + ∣ x ∣ ) s i n [ x ]}{∣ x ∣}

is equal to

Answer: (B)

x \to 0^{+}

, for

0 < x < 1

the greatest integer

[x] = 0

and

∣ x ∣ = x

, so

sin [x] = sin 0 = 0

. The expression then becomes

\frac{x ( 0 + x ) \cdot 0}{x} = 0

for every such

x

, so the right-hand limit is simply

0

JEE Main · 2019 · 09 Jan 2019 · Shift 2 · Single correct option

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