## Ceiling and floor functions: IITJEE mains training

Problem 1:

For what values of x, is (a) (b) ?

Problem 2:

Which real numbers x satisfy the equation ?

Problem 3:

Does for all real x? Give reasons for your answer.

Problem 4:

Graph: when ; and , when .

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

Cheers,

Nalin Pithwa

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