Question

Evaluate $\lim_{x \to \infty}x^4\left(\arctan\frac{2x^2+5}{x^2+1}-\arctan\frac{2x^2+7}{x^2+2}\right)$

score 86 · Answer 1 · 2026-04-16 16:16:57

86

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Evaluate $\lim_{x \to \infty}x^4\left(\arctan\frac{2x^2+5}{x^2+1}-\arctan\frac{2x^2+7}{x^2+2}\right)$

Published on 16 Apr 2026 - 16:16

score 187 · Answer 2 · 2026-04-08 23:28:18

187

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Algebraic proof involving Independent Set Problem & Maximum Degree

Published on 08 Apr 2026 - 23:28

score 406 · Answer 3 · 2026-04-10 23:31:06

406

Views

Closed sets in induced metric space

Published on 10 Apr 2026 - 23:31

score 42 · Answer 4 · 2026-04-16 15:16:22

42

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Just using x for proving any real interval is uncountable

Published on 16 Apr 2026 - 15:16

score 72 · Answer 5 · 2026-04-17 12:39:47

72

Views

Verify proofs related to monotonicity of $x_{n+1} = {1\over 2}(x_n+y_n)$ and $y_{n+1} = \sqrt{{1\over 2}(x_n^2 + y_n^2)}$

Published on 17 Apr 2026 - 12:39

score 85 · Answer 6 · 2026-04-13 21:34:20

85

Views

Is my Proof Correct: $(X, \mathcal{A}, \mu)$ $\sigma-$finite measure space then $\mu^{*}(B) < \infty$

Published on 13 Apr 2026 - 21:34

score 44 · Answer 7 · 2026-04-15 05:39:02

44

Views

Proving $(\overline{A})'=A'$ if $(X,\tau)$ for $T_1$.

Published on 15 Apr 2026 - 5:39

score 562 · Answer 8 · 2026-04-14 13:56:38

562

Views

Generalize Jensen's Integral Inequality to the product of two functions

Published on 14 Apr 2026 - 13:56

score 217 · Answer 9 · 2026-04-15 19:16:16

217

Views

Counterexample of the converse of Jensen's inequality

Published on 15 Apr 2026 - 19:16

score 41 · Answer 10 · 2026-04-13 16:10:38

41

Views

Laurent series $f(z)=\frac{\sqrt{z}}{z+i}$

Published on 13 Apr 2026 - 16:10

score 1.8k · Answer 11 · 2026-04-17 01:44:45

1.8k

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Using Parseval's identity to show that $\frac{\pi^2}{8}=1+\frac{1}{3^2}+\frac{1}{5^2}+\frac{1}{7^2}+...$

Published on 17 Apr 2026 - 1:44

score 445 · Answer 12 · 2026-04-12 02:00:29

445

Views

Finding probability with Law of Total Probability and Bayes Theorem

Published on 12 Apr 2026 - 2:00

score 44 · Answer 13 · 2026-04-13 20:55:38

44

Views

Probability of equal # of blue and red fish chosen when drawing without replacement

Published on 13 Apr 2026 - 20:55

score 94 · Answer 14 · 2026-04-11 23:24:51

94

Views

Show existence of holomorphic function $h$ such that $e^{h(z)}=1+z^5+z^{10}$

Published on 11 Apr 2026 - 23:24

score 84 · Answer 15 · 2026-04-16 14:45:01

84

Views

Compute the cardinality of a field $K$ and show that $K$ contains a splitting field of $X^{31} - 1$

Published on 16 Apr 2026 - 14:45

List Question

Evaluate $\lim_{x \to \infty}x^4\left(\arctan\frac{2x^2+5}{x^2+1}-\arctan\frac{2x^2+7}{x^2+2}\right)$

Algebraic proof involving Independent Set Problem & Maximum Degree

Closed sets in induced metric space

Just using x for proving any real interval is uncountable

Verify proofs related to monotonicity of $x_{n+1} = {1\over 2}(x_n+y_n)$ and $y_{n+1} = \sqrt{{1\over 2}(x_n^2 + y_n^2)}$

Is my Proof Correct: $(X, \mathcal{A}, \mu)$ $\sigma-$finite measure space then $\mu^{*}(B) < \infty$

Proving $(\overline{A})'=A'$ if $(X,\tau)$ for $T_1$.

Generalize Jensen's Integral Inequality to the product of two functions

Counterexample of the converse of Jensen's inequality

Laurent series $f(z)=\frac{\sqrt{z}}{z+i}$

Using Parseval's identity to show that $\frac{\pi^2}{8}=1+\frac{1}{3^2}+\frac{1}{5^2}+\frac{1}{7^2}+...$

Finding probability with Law of Total Probability and Bayes Theorem

Probability of equal # of blue and red fish chosen when drawing without replacement

Show existence of holomorphic function $h$ such that $e^{h(z)}=1+z^5+z^{10}$

Compute the cardinality of a field $K$ and show that $K$ contains a splitting field of $X^{31} - 1$

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