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Prove that ${\lim_{n\to\infty}\frac{2n-1}{n+1}}=2.$

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#limits #proof-verification #epsilon-delta
66
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Another $\varepsilon$-$\delta$ argument for $h(x)=\frac{1}{1+x^2}$

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#real-analysis #continuity #epsilon-delta
1.1k
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Does certain open cover for rationals numbers in [0,1] cover the whole set?

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#real-analysis #measure-theory #epsilon-delta #rational-numbers
3.3k
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Find the limit $\lim_{n \to \infty} \frac {2n^2+10n+5}{n^2}$ and prove it.

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#real-analysis #sequences-and-series #limits #proof-verification #epsilon-delta
83
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Proving the limit of a sequence

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#sequences-and-series #epsilon-delta
70
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Functions satisfying $ \forall x \in E: \exists \delta > 0: \forall y \in E \cap (x,x+\delta): f(x) \le f(y)$

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#analysis #continuity #epsilon-delta #monotone-functions
156
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Delta epsilon proof of convergence for $a_n = \frac{2-2n}{(n^2+n)(n^2-3)}$

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#calculus #epsilon-delta
77
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Proving that $f(x)=x^2$ is uniformly continuous on any closed interval, but not on $\mathbb{R}$

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#calculus #proof-verification #continuity #epsilon-delta #uniform-continuity
58
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Epsilon Delta Proof help

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#functions #proof-writing #epsilon-delta
30
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Verification of Epsilon-Delta proof.

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#real-analysis #limits #proof-verification #epsilon-delta
142
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$\epsilon$-$\delta$ proof that $\lim\limits_{x \to 1} 2^{-\frac{1}{(x-1)^2}} = 0$

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#real-analysis #epsilon-delta
654
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How to find $\lim\limits_{x\to +\infty} \frac{x^{2}e^{-x}}{x^{2}+1}\sin(xe^{x^{2}})$?

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#calculus #limits #epsilon-delta
14.6k
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Prove that the sum of two continuous functions is continuous

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#real-analysis #calculus #continuity #solution-verification #epsilon-delta
42
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continuity of $f(x)=\frac{xy_0}{x^2+y_0^2}$ at $x_0$

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#calculus #real-analysis #epsilon-delta
346
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Showing that a function is Uniformly continuous

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#calculus #real-analysis #continuity #epsilon-delta #uniform-continuity

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