Let $f\left( x \right) = x\left[ x \right]$, where [x] denotes integral part of $x$. If $a$ is not an integer, then $\mathop {\lim }\limits_{h \to 0} \frac{{f\left( {a + h} \right) - f\left( a \right)}}{h} = $

JEE MATHEMATICS MCQ: LIMITS

1 Easy

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Application +4 | -1

Let

f\left( x \right) = x\left[ x \right]

, where [x] denotes integral part of

x

. If

a

is not an integer, then

\lim\limits_{h \to 0} \frac{{f\left( {a + h} \right) - f\left( a \right)}}{h} =

View answer and explanation

Correct option: C

[a]

Option C ([a]) is correct because since a is not an integer, for small h, [a+h] = [a], simplifying the limit calculation.

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