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  • MarkFL's Avatar
    Today, 15:28
    MarkFL replied to a thread Trigonometric Identity in Trigonometry
    An alternate approach would be to factor the LHS as the sum of two cubes: ...
    6 replies | 66 view(s)
  • MarkFL's Avatar
    Yesterday, 16:10
    MarkFL replied to a thread [SOLVED] 206.07.05.88 partial fractions??? in Calculus
    No, but either way will work, because of the commutative property of addition.. :D
    6 replies | 74 view(s)
  • MarkFL's Avatar
    Yesterday, 15:45
    MarkFL replied to a thread [SOLVED] 206.07.05.88 partial fractions??? in Calculus
    In the formula you've used, we have $a=1$...and so after back-substituting for $u$: I=\arctan\left(\sqrt{x^2+4x+3}\right)+C
    6 replies | 74 view(s)
  • MarkFL's Avatar
    Yesterday, 14:51
    As long as the radical is not a factor in a denominator (in that case the radicand cannot be zero), then yes that rule can be applied for domain...
    17 replies | 217 view(s)
  • MarkFL's Avatar
    Yesterday, 14:15
    Even though Pre-Calculus is taught in universities, it's really considered a remedial course at that level, and so that's why we classify it as a...
    17 replies | 217 view(s)
  • MarkFL's Avatar
    June 26th, 2017, 15:42
    Let's look at the graph as advised: y=x^4-4x^3+6x^2-4x+2 Based on this, what values of $x$ appear to satisfy the two given inequalities? By...
    2 replies | 41 view(s)
  • MarkFL's Avatar
    June 26th, 2017, 15:39
    Yes, observe that the root $x=0$ is of even multiplicity (4), and so the sign of the expression will not change across this root. The others are of...
    3 replies | 45 view(s)
  • MarkFL's Avatar
    June 26th, 2017, 15:35
    Yes, you should wind up with: \frac{(x+1)(x-6)}{x-1}\ge0 And then observing we have a weak inequality, and that $x=1$ must be excluded...
    3 replies | 43 view(s)
  • MarkFL's Avatar
    June 26th, 2017, 13:40
    MarkFL replied to a thread Words By Kurt Kaiser in Chat Room
    I really just wanted to point out the fallacious nature of incredulity as an argument for anything. :D
    10 replies | 136 view(s)
  • MarkFL's Avatar
    June 26th, 2017, 12:54
    It has no rational roots, but we can use the quadratic formula to state: x^3=\frac{3\pm\sqrt{5}}{2}\implies x=\sqrt{\frac{3\pm\sqrt{5}}{2}} ...
    9 replies | 98 view(s)
  • MarkFL's Avatar
    June 26th, 2017, 12:48
    MarkFL replied to a thread Words By Kurt Kaiser in Chat Room
    It was the study of the Bible (among other things), which I have read through several times, that actually helped drive my skepticism during my...
    10 replies | 136 view(s)
  • MarkFL's Avatar
    June 26th, 2017, 11:20
    MarkFL replied to a thread Words By Kurt Kaiser in Chat Room
    The "argument" given in the OP, and which I was addressing, was exactly that simple from what I saw: "all of this beauty both near and afar,...
    10 replies | 136 view(s)
  • MarkFL's Avatar
    June 26th, 2017, 10:27
    MarkFL replied to a thread Words By Kurt Kaiser in Chat Room
    The main point I was addressing is that which I've heard more than once in my life, which goes something like: I look at the world, with it's...
    10 replies | 136 view(s)
  • Evgeny.Makarov's Avatar
    June 26th, 2017, 09:29
    Evgeny.Makarov replied to a thread Jokes in Chat Room
    1. Beethoven, being deaf, could write wonderful symphonies. Why can't I, being dumb, write good research papers? 2. One couple used to stop at a...
    161 replies | 19522 view(s)
  • MarkFL's Avatar
    June 26th, 2017, 01:50
    MarkFL replied to a thread Words By Kurt Kaiser in Chat Room
    For what it's worth, this is what's know as an Argument from incredulity. It's a fairly common logical fallacy made by those who try to argue...
    10 replies | 136 view(s)
  • MarkFL's Avatar
    June 26th, 2017, 00:31
    One of the proven assertions of the FTOA is: A polynomial of degree n will have exactly n roots (counting multiplicity). That's why I...
    9 replies | 98 view(s)
  • MarkFL's Avatar
    June 25th, 2017, 22:14
    MarkFL replied to a thread Words By Kirk Talley in Chat Room
    That puts me in mind of "Enter Sandman" by Metallica: Hush little baby, don't say a word And never mind that noise you heard It's just the...
    1 replies | 37 view(s)
  • MarkFL's Avatar
    June 25th, 2017, 21:53
    The solution is: \,\cup\, You missed an interval because -2 is not in the interval ... (an alarm should have gone off in your head when you saw...
    8 replies | 87 view(s)
  • MarkFL's Avatar
    June 25th, 2017, 19:43
    What you should have is: \frac{x^6-3x^3+1}{x^3}\ge0 Recall, you don't want to multiply an inequality by an expression having an unknown sign. ...
    9 replies | 98 view(s)
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    Would it be possible if you helped me on a thread in the Trigonometry Forum? I am still stumped.
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    Thanks so much evinda!
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    Thanks evinda , sorry for late reply. I am busy with exams these days.
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    Thank you very much, evinda!
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    Hey evinda,

    I think if you ask for the proof of FLT for n = 4 in a different thread it would be better as it would be off-topic on the current thread. If you post it as a separate question, I'd be more than willing to answer to it.
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    Thank you very much!!!
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    Thanks, but I would have liked to stay 13.
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    Hello and welcome to MHB, evinda!

    If you have any questions or comments about the forums, please feel free to address them to me or another staff member. We are happy to help, and look forward to your participation here!

    Best Regards,

    Mark.
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