List questions from ceiling-and-floor-functions

Published on 10 Jun 2016 - 21:26

988

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Limit of floor function

Published on 14 Jun 2016 - 22:28

112

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Property of the floor function

Published on 15 Jun 2016 - 8:04

115

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Is the limit $\lim_{x\rightarrow0}\frac{\sin{[x]}}{[x]}$ a one sided limit or not?

Published on 17 Jun 2016 - 15:13

549

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Removing jump discontinuity from a tricky function.

Published on 26 Mar 2026 - 1:29

1.1k

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How can I remove the floor function from ⌊ab/10⌋?

Published on 22 Jun 2016 - 20:26

193

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Evaluation of $\bigg[ \lim_{x\to 0} \frac{e-(1+x)^{1/x}}{\tan x}\bigg]$

Published on 23 Jun 2016 - 23:50

173

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Solve in integers the equation $\left\lfloor\frac{x^2-y^3}{x+y^2} \right\rfloor=1+x-y$

Published on 24 Jun 2016 - 5:52

773

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A form for a piecewise continuous function?

Published on 01 Apr 2026 - 20:59

218

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Value of $z$ in the given system of equations

Published on 28 Mar 2026 - 12:14

310

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What is $\sum_{i=0}^n \left\lfloor \sqrt{i}\right\rfloor \binom{n}{i}$?

Published on 28 Jun 2016 - 17:55

46

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Analyzing and plotting function $f(x)=\lfloor\frac{3-x}{1+x^2}\rfloor$?

Published on 29 Jun 2016 - 16:27

132

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Find all integers $p>q\ge 0$, such that for all real $x,y \in [0;1]$ following inequality holds $[px]+[py]\ge [qx+y]+[x+qy]$

Published on 01 Jul 2016 - 12:07

229

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Evaluate $\int_{0}^{\infty} (-1)^{\lfloor x\rfloor}\cdot e^{-x} dx $

Published on 05 Jul 2016 - 11:14

5.2k

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Prove the following ceiling and floor identities?

Published on 09 Apr 2013 - 17:59

List Question

Solutions to $\lfloor 2x\rfloor-\lfloor x+1\rfloor=2x$

Limit of floor function

Property of the floor function

Is the limit $\lim_{x\rightarrow0}\frac{\sin{[x]}}{[x]}$ a one sided limit or not?

Removing jump discontinuity from a tricky function.

How can I remove the floor function from ⌊ab/10⌋?

Evaluation of $\bigg[ \lim_{x\to 0} \frac{e-(1+x)^{1/x}}{\tan x}\bigg]$

Solve in integers the equation $\left\lfloor\frac{x^2-y^3}{x+y^2} \right\rfloor=1+x-y$

A form for a piecewise continuous function?

Value of $z$ in the given system of equations

What is $\sum_{i=0}^n \left\lfloor \sqrt{i}\right\rfloor \binom{n}{i}$?

Analyzing and plotting function $f(x)=\lfloor\frac{3-x}{1+x^2}\rfloor$?

Find all integers $p>q\ge 0$, such that for all real $x,y \in [0;1]$ following inequality holds $[px]+[py]\ge [qx+y]+[x+qy]$

Evaluate $\int_{0}^{\infty} (-1)^{\lfloor x\rfloor}\cdot e^{-x} dx $

Prove the following ceiling and floor identities?

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