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Big $O$ and Big $\Theta$ proof

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#discrete-mathematics #asymptotics
1.2k
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How many edges does an Erdős-Rényi graph have to have, to almost surely have a component with multiple cycles?

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#probability #graph-theory #asymptotics #random-graphs
496
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Sum $S(n,c) = \sum_{i=1}^{n-1}\dfrac{i}{ci+(n-i)}$

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#sequences-and-series #inequality #asymptotics
1.3k
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Prove that a circle has an infinite number of tangents

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#algebra-precalculus #asymptotics #circles
423
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Growth rate of $1/(\log(x)-\log(x-1))$

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#algebra-precalculus #asymptotics #logarithms
398
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Asymptotic expansion of $J(t) = \int^{\infty}_{0}{\exp(-t(x + 4/(x+1)))}\, dx$

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#integration #sequences-and-series #asymptotics #special-functions #power-series
59
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Big - Oh proof $n^{2^n} = O(2^{2^n})$

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#asymptotics
275
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Fnding horizontal asymptotes of $f(x)= \sqrt {9x^2+2x}-3x$

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#calculus #asymptotics #gre-exam
506
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Asymptotic expansion for harmonic sum in two variables

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#sequences-and-series #number-theory #asymptotics
112
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How to prove that there are $O(T\ln T)$ zeros in the critical strip of the Riemann zeta function?

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#asymptotics #roots #riemann-zeta
1.1k
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Need help analyzing a merge sort

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#discrete-mathematics #asymptotics #recurrence-relations #sorting
265
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big O notation - explain the equality

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#asymptotics
60
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Asymptotically evaluating integrals with oscillatory behaviour in both numerator and denominator

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#asymptotics
4.8k
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Find the asymptotic tight bound for $T(n) = 4T(n/2) + n^{2}\log n$

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#recurrence-relations #asymptotics
35
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Find the order of the following expression as x->0

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#asymptotics #taylor-expansion

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