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  • MarkFL's Avatar
    Today, 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,...
    6 replies | 47 view(s)
  • MarkFL's Avatar
    Today, 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...
    6 replies | 40 view(s)
  • MarkFL's Avatar
    Today, 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) ...
    4 replies | 56 view(s)
  • MarkFL's Avatar
    Today, 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...
    6 replies | 47 view(s)
  • MarkFL's Avatar
    Today, 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...
    6 replies | 40 view(s)
  • MarkFL's Avatar
    Today, 02:30
    This is a calculus question...please don't continue to post calculus questions in other forums. If given: ...
    3 replies | 78 view(s)
  • MarkFL's Avatar
    Yesterday, 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:...
    6 replies | 47 view(s)
  • MarkFL's Avatar
    Yesterday, 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} ...
    6 replies | 40 view(s)
  • Euge's Avatar
    Yesterday, 19:07
    No, but one argues that a monotone function on a closed interval $$ belongs to $R$. So then $F$ would make sense. Use an $\epsilon-\delta$ argument...
    5 replies | 124 view(s)
  • MarkFL's Avatar
    Yesterday, 16:18
    MarkFL replied to a thread The Distance Across in Geometry
    Using the Pythagorean theorem, we find: \overline{MK}=\sqrt{(\sqrt{2}a)^2+(\sqrt{2}b)^2}=\sqrt{2\left(a^2+b^2\right)} Now, we know that...
    6 replies | 63 view(s)
  • MarkFL's Avatar
    Yesterday, 06:10
    MarkFL replied to a thread [SOLVED] Minimum of function under constraint in Calculus
    I would use W|A: W|A - optimize 2x+y subject to xy=18
    8 replies | 249 view(s)
  • MarkFL's Avatar
    Yesterday, 04:29
    The objective function is linear, so it describes a plane, and so I don't believe there will be any saddle points, or in fact any critical points...
    4 replies | 60 view(s)
  • MarkFL's Avatar
    Yesterday, 04:04
    MarkFL replied to a thread Boat direction in Calculus
    Is this a calculus-based physics course?
    6 replies | 91 view(s)
  • MarkFL's Avatar
    Yesterday, 01:37
    What I would do is observe that we have cyclical symmetry, that is we may interchange $x_1$ and $x_2$ with no change in either the objective function...
    4 replies | 60 view(s)
  • MarkFL's Avatar
    Yesterday, 01:25
    MarkFL replied to a thread The Distance Across in Geometry
    Not quite...it would be \sqrt{2}a and \sqrt{2}b...so what would the diagonal of the rectangle be?
    6 replies | 63 view(s)
  • MarkFL's Avatar
    March 23rd, 2017, 21:17
    MarkFL replied to a thread The Distance Across in Geometry
    I would let $a$ be the length (in cm) of the segments with 1 tick mark, and $b$ be the length (in cm) of the segments with 2 tick marks. And so,...
    6 replies | 63 view(s)
  • MarkFL's Avatar
    March 23rd, 2017, 19:30
    MarkFL replied to a thread Boat direction in Calculus
    Being that it is an optimization problem, on a function in two variables, the way I worked it using the calculus is the most straightforward way I...
    6 replies | 91 view(s)
  • MarkFL's Avatar
    March 23rd, 2017, 12:53
    MarkFL replied to a thread Boat direction in Calculus
    I think what I would do is orient a coordinate system such that south is up and west is to the right. At time $t=0$, have boat A at the origin, and...
    6 replies | 91 view(s)
  • MarkFL's Avatar
    March 23rd, 2017, 11:28
    There are online calculators that will spit out the answer to this question, however if you want genuine help, we need to know what you've tried, or...
    3 replies | 102 view(s)
  • Euge's Avatar
    March 23rd, 2017, 11:20
    Euge replied to a thread [SOLVED] {10.7.37 find the radius of convergence in Calculus
    Well, the coefficient $a_n$ of $x^n$ in the power series reduces to $6^n$, for $6\cdot 12\cdot 18\cdots 6n = (6\cdot 1)(6\cdot 2)\cdots (6\cdot n) =...
    3 replies | 62 view(s)
  • MarkFL's Avatar
    March 23rd, 2017, 03:19
    MarkFL replied to a thread Factoring...3 in Pre-Calculus
    Finding what to multiply together to get an expression. It is like "splitting" an expression into a multiplication of simpler expressions.
    6 replies | 74 view(s)
  • MarkFL's Avatar
    March 23rd, 2017, 02:50
    MarkFL replied to a thread Factoring...3 in Pre-Calculus
    I would say division is the inverse of multiplication, but factoring is certainly related to division. For example, we know: ...
    6 replies | 74 view(s)
  • MarkFL's Avatar
    March 23rd, 2017, 02:42
    MarkFL replied to a thread Factoring...4 in Pre-Calculus
    Looks good. (Yes)
    2 replies | 34 view(s)
  • MarkFL's Avatar
    March 23rd, 2017, 02:32
    MarkFL replied to a thread Factoring...3 in Pre-Calculus
    Perfect. (Yes)
    6 replies | 74 view(s)
  • MarkFL's Avatar
    March 23rd, 2017, 02:24
    MarkFL replied to a thread Factoring...2 in Pre-Calculus
    I was just rewriting that term as a perfect square: 9(ab+c)^2=3^2(ab+c)^2=(3(ab+c))^2
    4 replies | 47 view(s)
  • MarkFL's Avatar
    March 23rd, 2017, 02:16
    MarkFL replied to a thread Factoring...2 in Pre-Calculus
    I would first write the expression as: (2ab)^2-(3(ab+c))^2 Now, factor as the difference of squares, and simplify. :D
    4 replies | 47 view(s)
  • Euge's Avatar
    March 23rd, 2017, 01:50
    For the sake of completion, I'll post a complete answer. Let $X$ be a first countable Hausdorff space. Fix $x\in X$, and let $\{B_n\}_{n\in \Bbb N}$...
    2 replies | 123 view(s)
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    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?
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    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!
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    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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