_ x 3 ,[x] = , (where [.] = greatest integer function) - Vidyadip

MCQ

$\mathop {\lim }\limits_{x \to 3} \,[x] = $, (where $[.] =$ greatest integer function)

A
$2$
B
$3$
✓
Does not exist
D
None of these

✓

Answer

Correct option: C.

Does not exist

c
(c) $\mathop {\lim }\limits_{h \to {0^ + }} \,[3 + h] = 3$ and $\mathop {\lim }\limits_{h \to {0^ - }} \,[3 - h] = 2$

$\therefore$ $\mathop {\lim }\limits_{x \to 3} \,\,[x]$ does not exist.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The set of values of $‘a’$ which satisfy the equation

$\int\limits_0^2 {(t - {{\log }_2}a)\,dt} $ $= log_2$ $\left( {\frac{4}{{{a^2}}}} \right)$ is

Let sets $A$ and $B$ have $5$ elements each. Let the mean of the elements in sets $A$ and $B$ be $5$ and $8$ respectively and the variance of the elements in sets $A$ and $B$ be $12$ and $20$ respectively $A$ new set $C$ of $10$ elements is formed by subtracting $3$ from each element of $A$ and adding 2 to each element of B. Then the sum of the mean and variance of the elements of $C$ is $.......$.

The equation of the line bisecting the line segment joining the points $(a, b)$ and $(a',\;b')$ at right angle, is

The distance between the line $r = 2i - 2j + 3k + \lambda (i - j + 4k)$ and the plane $r.(i + 5j + k) = 5$ is

The number of ordered pairs $(a, b)$ of intege such that $a-b$ is a root of $x^2+a x+b=0$ is

A box contains $25$ tickets numbered $1, 2, ....... 25$. If two tickets are drawn at random then the probability that the product of their numbers is even, is

The differential equation of all straight lines passing through the point $(1,\, - 1)$ is

If ${ }^{n} P_{r}={ }^{n} P_{r+1}$ and ${ }^{n} C_{r}={ }^{n} C_{r-1}$, then the value of $r$ is equal to:

The total number of terms in the expansion of ${(x + a)^{100}} + {(x - a)^{100}}$ after simplification will be

The length of the normal chord to the parabola ${y^2} = 4x$, which subtends right angle at the vertex is