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  • Ackbach's Avatar
    Today, 10:17
    Through the Red Hat Developers program, which is a free and very easy sign-up, you can freely download and install Red Hat Enterprise Linux Server....
    0 replies | 23 view(s)
  • Euge's Avatar
    Yesterday, 16:32
    Hi FallArk, The function in part (c) is not differentiable at $x = c$, for it is discontinuous at that point. Just check the one-sided limits. ...
    3 replies | 69 view(s)
  • MarkFL's Avatar
    Yesterday, 12:24
    Just to follow up, here is the completed table: Sum $S$ Probability of $S$: $P(S)$ Net Gain/Loss (in dollars) $G$ Product $G\cdot P(S)$
    2 replies | 79 view(s)
  • Euge's Avatar
    March 26th, 2017, 22:53
    Euge replied to a thread [SOLVED] Real Analysis in Analysis
    No. Use the conditions $f \ge 0$ and $\int_a^b f = 0$, along with basic properties of the integral to prove that result.
    12 replies | 181 view(s)
  • MarkFL's Avatar
    March 26th, 2017, 22:32
    MarkFL replied to a thread Radius of Circle in Pre-Calculus
    That is the radius of the circle after it has been increased by $a$ units. If I tell you that my weight increased by 20 lbs., then you know my...
    4 replies | 84 view(s)
  • Jameson's Avatar
    March 26th, 2017, 22:19
    Hi tmt, (Wave) For the quoted part in bold, should this read "If all cars are reserved for the day..."? I think there are two events here,...
    1 replies | 49 view(s)
  • MarkFL's Avatar
    March 26th, 2017, 21:35
    MarkFL replied to a thread Radius of Circle in Pre-Calculus
    Let's let $0<a$ be the number units the radius must be increased. And so the change in area we can write as: \Delta A=\pi(r+a)^2-\pi r^2=b Now...
    4 replies | 84 view(s)
  • Euge's Avatar
    March 26th, 2017, 21:25
    Euge replied to a thread Ball Application in Pre-Calculus
    Yes. Yes.
    2 replies | 40 view(s)
  • Euge's Avatar
    March 26th, 2017, 21:19
    Euge replied to a thread Find All Real Solutions in Pre-Calculus
    Yes, it's correct.
    2 replies | 55 view(s)
  • Euge's Avatar
    March 26th, 2017, 21:15
    Euge replied to a thread [SOLVED] Real Analysis in Analysis
    Almost. You have a typo in the last line: the fraction $\frac{x + h - h}{h}$ should be $$\frac{x + h - \color{red}{x}}{h}$$
    12 replies | 181 view(s)
  • Euge's Avatar
    March 26th, 2017, 12:39
    Euge replied to a thread [SOLVED] Real Analysis in Analysis
    To prove problem 1 directly, fix $x\in $ and show that $$f(x) = \lim_{h\to 0^+} \frac{1}{h}\int_x^{x+h} f(t)\, dt$$ Then show that for all...
    12 replies | 181 view(s)
  • Euge's Avatar
    March 26th, 2017, 02:05
    Euge replied to a thread [SOLVED] Real Analysis in Analysis
    Well, the difference between the Riemann sum and integral is made less than $\epsilon$ in magnitude when $n\ge N$, but since $\epsilon$ was...
    12 replies | 181 view(s)
  • Euge's Avatar
    March 26th, 2017, 01:53
    Euge replied to a thread [SOLVED] Real Analysis in Analysis
    Not quite. Fix $k$. If $n \ge N$ and $x\in \left$, then $\lvert \frac{k}{n} - x\rvert \le \frac{1}{n} \le \frac{1}{N} < \delta$. Thus, for all $n \ge...
    12 replies | 181 view(s)
  • Euge's Avatar
    March 26th, 2017, 00:35
    Euge replied to a thread [SOLVED] Real Analysis in Analysis
    Hi joypav, You're not bothering us with your questions, so feel free to ask whenever you have trouble. :)
    12 replies | 181 view(s)
  • Euge's Avatar
    March 25th, 2017, 23:17
    Yes. Let $h > 0$ such that $c + h\in (a,b)$. Then $$F(c + h) - F(c) - f(c+)h = \int_c^{c+h} \, dt $$ Let $\epsilon > 0$. There exists a $\delta...
    7 replies | 173 view(s)
  • MarkFL's Avatar
    March 25th, 2017, 21:53
    MarkFL replied to a thread The Distance Across in Geometry
    \overline{MK}=\sqrt{(\sqrt{2}a)^2+(\sqrt{2}b)^2}=\sqrt{2\left(a^2+b^2\right)}=\sqrt{2(50)}=\sqrt{100}=10 :D
    8 replies | 91 view(s)
  • MarkFL's Avatar
    March 25th, 2017, 21:07
    MarkFL replied to a thread Lagrange Multipliers 2 in Calculus
    I arbitrarily chose another point on the constraint, so that we could do a comparison like I mentioned just now in the other thread. :D
    9 replies | 90 view(s)
  • MarkFL's Avatar
    March 25th, 2017, 21:04
    MarkFL replied to a thread Lagrange Multipliers in Calculus
    I chose the point as it is on the constraint. Using that point, we can determine if our one critical point is a maximum or a minimum. If the...
    9 replies | 75 view(s)
  • Ackbach's Avatar
    March 25th, 2017, 20:02
    Here is this week's POTW: ----- Let $f$ be a real function with a continuous third derivative such that $f(x),f'(x), f''(x), f'''(x)$ are...
    0 replies | 34 view(s)
  • Ackbach's Avatar
    March 25th, 2017, 20:00
    We first note that \ Subtracting $S$ from this gives two sums, one of which is \ and the other of which sums to $xy^3/$. Therefore...
    1 replies | 74 view(s)
  • MarkFL's Avatar
    March 25th, 2017, 19:21
    MarkFL replied to a thread Lagrange Multipliers 2 in Calculus
    I agree that the point $(2,2)$, is the only one that meets all criteria. Now we need to compare the value of $f$ at another point on the constraint,...
    9 replies | 90 view(s)
  • MarkFL's Avatar
    March 25th, 2017, 19:08
    MarkFL replied to a thread Lagrange Multipliers in Calculus
    I agree that of the 3 critical points, $(1,1)$ is the only one in quadrant I. Now, we know this is either a maximum or a minimum, and to determine...
    9 replies | 75 view(s)
  • MarkFL's Avatar
    March 25th, 2017, 11:15
    MarkFL replied to a thread Factoring...6 in Pre-Calculus
    It might be more clear to state something like the following: The difference of cubes formula states: p^3-q^3=(p-q)\left(p^2+pq+q^2\right) ...
    5 replies | 77 view(s)
  • MarkFL's Avatar
    March 25th, 2017, 10:47
    MarkFL replied to a thread Lagrange Multipliers 2 in Calculus
    Consider: e^u=0 What do you get when solving for $u$? Okay, you correctly found $x^2=y^2$...what do you get when you substitute for...
    9 replies | 90 view(s)
  • MarkFL's Avatar
    March 25th, 2017, 10:39
    MarkFL replied to a thread Lagrange Multipliers in Calculus
    What I would do is use the constraint to determine $y=2-x$. Now substitute for $y$ in both equations you mentioned, and solve for $x$, then your...
    9 replies | 75 view(s)
  • MarkFL's Avatar
    March 25th, 2017, 02:30
    This is a calculus question...please don't continue to post calculus questions in other forums. If given: ...
    3 replies | 87 view(s)
  • MarkFL's Avatar
    March 24th, 2017, 23:12
    MarkFL replied to a thread Lagrange Multipliers 2 in Calculus
    If you solve both equations for $\lambda$ and then equate the results, you obtain: \frac{ye^{xy}}{2x}=\frac{xe^{xy}}{2y} Multiply through by 2:...
    9 replies | 90 view(s)
  • MarkFL's Avatar
    March 24th, 2017, 21:24
    MarkFL replied to a thread Lagrange Multipliers in Calculus
    Okay, so what this implies is: \frac{x}{\sqrt{6-x^2-y^2}}=\frac{y}{\sqrt{6-x^2-y^2}} Cross-multiply: x\sqrt{6-x^2-y^2}=y\sqrt{6-x^2-y^2} ...
    9 replies | 75 view(s)
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36 Visitor Messages

  1. Reply/View Conversation
    Yes caffeinemachine, I have a different solution of my own. I would have posted it along with johng's yesterday, but I was in a hurry, as I needed to get other things done. I might post it later today.
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    Thank you! It's been a bit hectic, what with moving to Kansas, and all. But I did have a great birthday.
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    Hi caffeinemachine. Very sorry that this is happening. Could you make a thread in our feedback forum describing what is happening when you get a moment? We will try to fix it ASAP.
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    My interests lie in dispersive wave equations and geometric analysis. You have a pretty interesting combination: combinatorics and geometry. So will you do combinatorial geometry or geometric combinatorics?
  5. Reply/View Conversation
    Hi caffeinemachine! I just wanted to wish you a happy birthday, and I hope you're having a great time.
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    Hey, just wanted to thank you. I didn't know the command \widehat existed until I saw you using it in your question about modules. Hope you get an answer, haha.

    Best wishes.
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    Happy Birthday, my friend!
  8. Reply/View Conversation
    Hi AK,

    I wish you luck, happiness, health and safety today, tomorrow and beyond...

    As you look back on yesterday, may your memories be warm ones. As you celebrate today, may your heart be filled with happiness and joy. As you look ahead to tomorrow, may your deepest hopes and dreams come true for you!

    I wish that for every extra candle on your cake, you receive an extra reason to smile. Happy Birthday to you!
  9. Reply/View Conversation
    Hi, I'm currently traveling but will get back to you later today. Thank you for your patience!
  10. Reply/View Conversation
    That's very kind of you. Thanks
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About caffeinemachine

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April 13, 1991 (25)
About caffeinemachine
Biography:
I obtained a master's degree in mechanical engineering in May 2014.
Then I went on to join a master's programme in mathematics and obtained a master's degree in July 2016. I am currently a first year PhD student in mathematics. I love fountain pens and am a die hard fan of the Prince of Persia 2008 video game.
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