Limits & Continuity: For each xinmathbb R , let [x] be the greatest integer less than or… | JEE Main 2019 | Yukti Vault

Yukti Vault

JEE Main 2019 (Online) 9th January Evening ShiftQuestion 1

For each $x\in\mathbb R$, let $[x]$ be the greatest integer less than or equal to $x$. Then $\lim_{x\to0^-}\frac{x([x]+|x|)\sin[x]}{|x|}$ is equal to

Limits & Continuity

$1$$0$$-\sin1$✓ Correct answer$\sin1$

Solution

For $x\to0^-$: $[x]=-1$, $|x|=-x$, so the expression is $\frac{x(-1-x)\sin(-1)}{-x}=-(1+x)\sin1\to-\sin1$.

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