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What is the value of $\lim _{x\to 0}\left\lfloor\frac{\tan x \sin x}{x^2}\right\rfloor$

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#calculus #limits #trigonometry #ceiling-and-floor-functions
223
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Floor-Ceil Properties

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#discrete-mathematics #ceiling-and-floor-functions
162
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When Is the Remainder Less Than The Quotient

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#number-theory #summation #ceiling-and-floor-functions
666
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odd prime division

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#number-theory #prime-numbers #ceiling-and-floor-functions
149
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How to evaluate the finite sequence (involving the floor function)?

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#summation #radicals #ceiling-and-floor-functions
204
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What floor function identity makes this true: $(-1)^{\lfloor x\rfloor} = -2\lfloor x\rfloor + 4\left\lfloor\frac {\lfloor x\rfloor}2\right\rfloor +1$?

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#algebra-precalculus #ceiling-and-floor-functions
6.8k
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Function with an asymptote at y=-1 and y=1

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#functions #asymptotics #ceiling-and-floor-functions
350
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Hermite's identity for sum of floor function

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#generating-functions #math-history #ceiling-and-floor-functions
895
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For all real numbers $x$, prove $\lfloor x - 2\rfloor = \lfloor x\rfloor - 2$

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#algebra-precalculus #ceiling-and-floor-functions
130
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How to solve mixed-integer problem?

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#inequality #integer-programming #ceiling-and-floor-functions #mixed-integer-programming
2.5k
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If $x$, $\{x\}$, $\lfloor x\rfloor$ are in G.P, find $x$.

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#quadratics #ceiling-and-floor-functions #geometric-progressions #fractional-part
861
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How to isolate a variable in a floor function?

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#algebra-precalculus #ceiling-and-floor-functions
272
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Iterating through the jump discontinuities of $f(x)$

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#ceiling-and-floor-functions #piecewise-continuity
156
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Integrating $\int^b_a [x]\,dx+\int^b_a [-x]\,dx$

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#calculus #integration #definite-integrals #ceiling-and-floor-functions
1.3k
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Function that produces sequence 112123123412345...

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#sequences-and-series #generating-functions #closed-form #ceiling-and-floor-functions

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