Ceiling and floor functions: IITJEE mains training

Problem 1:

For what values of x, is (a) $\lfloor x \rfloor =0$ (b) $\lceil x \rceil =0$ ?

Problem 2:

Which real numbers x satisfy the equation $\lfloor x \rfloor = \lceil x \rceil$ ?

Problem 3:

Does $\lceil (-x) \rceil = - (\lfloor x \rfloor)$ for all real x? Give reasons for your answer.

Problem 4:

Graph: $f(x)=\lfloor x \rfloor$ when $x \geq 0$ ; and $f(x) = \lceil x \rceil$ , when $x <0$ .

Why is f(x) called the integer part of x? Discuss the continuity and differentiability of f(x).

Cheers,

Nalin Pithwa

This entry was written by Nalin Pithwa, posted on September 26, 2019 at 12:11 pm, filed under calculus, IITJEE Mains. Bookmark the permalink. Follow any comments here with the RSS feed for this post. Post a comment or leave a trackback: Trackback URL.

Leave a Reply Cancel reply

Enter your comment here...

Fill in your details below or click an icon to log in:

Email (required) (Address never made public)

Name (required)

Website

You are commenting using your WordPress.com account. ( Log Out / Change )

You are commenting using your Google account. ( Log Out / Change )

You are commenting using your Twitter account. ( Log Out / Change )

You are commenting using your Facebook account. ( Log Out / Change )

Cancel

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

%d bloggers like this:

Mathematics Hothouse