gt6989b

reputation
310
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location       New York, NY
age            34
member for     1 year, 8 months
seen           12 hours ago
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|            |                  | bio          | visits                  |              |                  |
|------------|------------------|--------------|-------------------------|--------------|------------------|
|            | 2,688 reputation | website      | linkedin.com/in/gt6989b | member for   | 1 year, 8 months |
| 310 badges | location         | New York, NY | seen                    | 12 hours ago |                  |

307 Comments

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| 15h  | comment | Proof for an integral identity+1 - more general than my answer - I didn't want to bother with the integrals :)                                                                                                                                                                              |
| 15h  | comment | Proof for an integral identity@robjohn thanks, making the change.                                                                                                                                                                                                                           |
| 16h  | comment | How can I find all the solutions of $\sin^5x+\cos^3x=1$Substitute $\sin x = \sqrt{1 - \cos x}$ and solve the result in terms of $\cos x$. You could try to reduce $\cos x$ in terms of $\sin x$ as well.                                                                                    |
| 16h  | comment | Comparing $\sqrt{1001}+\sqrt{999}\ , \ 2\sqrt{1000}$You are asing to show that $\sqrt{x}$ is concave.                                                                                                                                                                                       |
| 17h  | comment | Formula for Sum of Logarithms $\ln(n)^m$@DonAntonio $\ln \left(n^{\ln n}\right) = \ln n \cdot \ln n = \ln^2 n$                                                                                                                                                                              |
| 18h  | comment | Formula for Sum of Logarithms $\ln(n)^m$Perhaps an idea - not sure if it will help. $$\sum \ln^2 n = \sum \ln n^{\ln n} = \ln \left( \prod n^{\ln n} \right).$$                                                                                                                             |
| 18h  | comment | Proof for an integral identityDo you mean $A=B$? Setting $f(x) = f(y) = 1$ as in the above hint yields $AB = A^2$...                                                                                                                                                                        |
| May7 | comment | Need an algorithm to compute number of elements in sample space@YevgeniyRozhkov for this case, i would condition on $z$ - it's either there or not, and if yes, choose a place for it. Now you reduced it to 2 elements and 2 or 3 places. 2 places are easy and for 3 you condition again. |
| May7 | comment | Evaluate using Riemann sums $\int_a^b \frac{1}{x^2}\mathrm{d}x$@darenn You're right, looks pretty nasty.                                                                                                                                                                                    |
| May7 | comment | Evaluate using Riemann sums $\int_a^b \frac{1}{x^2}\mathrm{d}x$What are you asking? How to evaluate the integral using riemann sums?                                                                                                                                                        |
| May7 | comment | A problem on calculating rank of a matrixIf all except one are $0$, then you get a $0$-matrix with one non-zero diagonal entry, which will have deteminant $0$.                                                                                                                             |
| May7 | comment | Simple fractions question@user2008436 I see, but a bit weird. My daughter learned solving 1st degree equations in 3rd grade (in the Russian math program), and I've heard the Singapore one is more advanced. Interesting.                                                                  |
| May6 | comment | Finding the error of the Taylor expansion of $\log(1 + x)$Write out the first couple of terms in the Taylor expansion of $\log(1+x)$ at $x=0$. Find $R_{0,k}$ and show that $R_{0,k} \to 0$ as $k \to \infty$.                                                                              |
| May6 | comment | In order to factor we must find its zeros?You can proceed to factor $(x-1)^2-2$ using $a^2-b^2=(a+b)(a-b)$ with $a=x-1$. (What is $b$?) As was pointed out by @TheChaz2.0, factoring and finding zeroes is equivalent.                                                                      |
| May3 | comment | Numerical estimation of simple integralI got the question. That is the definition of expected value of a function.                                                                                                                                                                          |
| May3 | comment | Numerical estimation of simple integralYou pick the function in such a way that $I = \mathbb{E}[f(U)]$, and then use Monte-Carlo, for example, to compute the expected value...                                                                                                             |
| May3 | comment | Considering the linear system Y'=AYTo take @julien's answer one step further, note that $AX=\lambda X$ is equivalent to $AX - \lambda X = 0$, which simplifies to $(A-\lambda I)X = 0$, which requires $det(A-\lambda I)=0$ if you want $X \neq 0$...                                       |
| May3 | comment | How to find equation of tangent line to $x^2 = 2y$ at $(-3, 9/2)$+1, this is clever :)                                                                                                                                                                                                      |
| May3 | comment | How to find equation of tangent line to $x^2 = 2y$ at $(-3, 9/2)$@Steven Please see the edit which explains the concept of the discriminant.                                                                                                                                                |
| May2 | comment | Overlapping AreasIf $a+b > c$, by Pigeonhole principle they overlap. Other than that, it is impossible to say - you may have $a = b = c/3$ and they overlap or not overlap, both are possible. Or perhaps I did not understand the problem?                                                 |
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