List questions from solution-verification

Published on 30 Mar 2020 - 14:14

101

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Evaluate the definite integral $\int_{-9}^9 (e^x-e^{-x}) dx$

Published on 30 Mar 2020 - 14:25

56

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Solution of the functional equation $f(x)f(y)=f(x+y)+xy$

Published on 30 Mar 2026 - 3:38

575

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Continuity of Translation Operator on Topological Vector Spaces

Published on 30 Mar 2020 - 15:01

75

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Integrating Factor and $\frac{dy}{dx}+y=3x$

Published on 25 Mar 2026 - 9:26

2.5k

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Prove that $\log(z_1z_2) = \log(z_1)+\log(z_2)$ for $z_1$, $z_2$ in the right half plane

Published on 30 Mar 2020 - 15:18

59

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Calculating $\mathbb{P}(A|\mathcal{G}) = \mathbb{E}(\mathbb{1}_A|\mathcal{G})$ for some $A$ and $\mathcal{G}$ - is my calculation correct?

Published on 02 Apr 2026 - 8:01

27

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Recursively defining stopping times for Doob's upcrossing estimate

Published on 27 Mar 2026 - 10:10

319

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The degree of splitting field of $X^4-2$ over $\mathbb Q$

Published on 26 Mar 2026 - 16:14

78

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If $L$ is semisimple, how is this ideal of $L$ semisimple?

Published on 06 Apr 2026 - 11:38

302

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Using Laplace transform to solve IVP involving complex roots

Published on 27 Mar 2026 - 13:20

132

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Telescoping series convergence/divergence with arctan

Published on 31 Mar 2020 - 2:39

55

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Given that $a+b+c=0$, show that $2(a^4+b^4+c^4)$ is a perfect square

Published on 31 Mar 2020 - 2:59

99

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Does my proof show that $\int _0^1\frac{dx}{x}$ converges?

Published on 07 Apr 2026 - 6:32

110

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If $ B(X) \ni \{T_n\} \to T $ invertible with $\|T_n^{−1}\|<1$ , then $T$ is invertible

Published on 31 Mar 2020 - 5:28

List Question

Evaluate the definite integral $\int_4^8 e^{4-x}dx$

Evaluate the definite integral $\int_{-9}^9 (e^x-e^{-x}) dx$

Solution of the functional equation $f(x)f(y)=f(x+y)+xy$

Continuity of Translation Operator on Topological Vector Spaces

Integrating Factor and $\frac{dy}{dx}+y=3x$

Prove that $\log(z_1z_2) = \log(z_1)+\log(z_2)$ for $z_1$, $z_2$ in the right half plane

Calculating $\mathbb{P}(A|\mathcal{G}) = \mathbb{E}(\mathbb{1}_A|\mathcal{G})$ for some $A$ and $\mathcal{G}$ - is my calculation correct?

Recursively defining stopping times for Doob's upcrossing estimate

The degree of splitting field of $X^4-2$ over $\mathbb Q$

If $L$ is semisimple, how is this ideal of $L$ semisimple?

Using Laplace transform to solve IVP involving complex roots

Telescoping series convergence/divergence with arctan

Given that $a+b+c=0$, show that $2(a^4+b^4+c^4)$ is a perfect square

Does my proof show that $\int _0^1\frac{dx}{x}$ converges?

If $ B(X) \ni \{T_n\} \to T $ invertible with $\|T_n^{−1}\|<1$ , then $T$ is invertible

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