Register

ISI2015-DCG-57

• retagged by
751 views
0 0 votes

Let $y=\lfloor x \rfloor$, where $\lfloor x \rfloor$ is greatest integer less than or equal to $x$. Then

  1. $y$ is continuous and many-one
  2. $y$ is not differentiable and many-one
  3. $y$ is not differentiable
  4. $y$ is differentiable and many-one

2 Answers

1 1 vote

The graph is discontinuos, so non-differentialble, and for two real numbers, a common image is there…

so Option B

0 0 votes

we all know that greatest integer function can't be continuous and differentiable at integer value 

The greatest integer function rounds any number down to the nearest integer. For example, 6.3 would get rounded down to 6, and 7.9 would get rounded down to 7. 
Voting & Accepting an answer helps improve the community
← Previous · ISI2015-DCG-58Next → · ISI2015-DCG-56
← Previous in category · ISI2015-DCG-58Next in category → · ISI2015-DCG-56
Position:
Show:

Related questions

1 1 vote
2 2 answers
1.5k
1.5k views
Arjun asked Sep 23, 2019
1,474 views
ISI2015-MMA-69
Consider the function $$f(x) = \begin{cases} \int_0^x \{5+ \mid 1-y \mid \} dy & \text{ if } x>2 \\ 5x+2 & \text{ if } x \leq 2 \end{cases}$$ Then$f$ is not continuous at...
0 0 votes
2 2 answers
1.3k
1.3k views
Arjun asked Sep 23, 2019
1,262 views
ISI2014-DCG-29
If $f(x) = \sin \bigg( \dfrac{1}{x^2+1} \bigg),$ then$f(x)$ is continuous at $x=0$, but not differentiable at $x=0$$f(x)$ is differentiable at $x=0$, and $f’(0) \neq 0$$f...
0 0 votes
0 0 answers
626
626 views
gatecse asked Sep 18, 2019
626 views
ISI2016-DCG-58
Let $y=\left \lfloor x \right \rfloor$ where $\left \lfloor x \right \rfloor$ is greatest integer less than or equal to $x$. Then$y$ is continuous and many-one.$y$ is not...
1 1 vote
2 2 answers
669
669 views
gatecse asked Sep 18, 2019
669 views
ISI2015-DCG-45
The value of $\underset{x \to 0}{\lim} \dfrac{\tan ^2 x – x \tan x }{\sin x}$ is$\frac{\sqrt{3}}{2}$$\frac{1}{2}$$0$None of these