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  • Euge's Avatar
    Yesterday, 22:53
    Euge replied to a thread 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 | 150 view(s)
  • MarkFL's Avatar
    Yesterday, 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 | 41 view(s)
  • Jameson's Avatar
    Yesterday, 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 | 38 view(s)
  • MarkFL's Avatar
    Yesterday, 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 | 41 view(s)
  • Euge's Avatar
    Yesterday, 21:25
    Euge replied to a thread Ball Application in Pre-Calculus
    Yes. Yes.
    2 replies | 25 view(s)
  • Euge's Avatar
    Yesterday, 21:19
    Euge replied to a thread Find All Real Solutions in Pre-Calculus
    Yes, it's correct.
    2 replies | 36 view(s)
  • Euge's Avatar
    Yesterday, 21:15
    Euge replied to a thread 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 | 150 view(s)
  • topsquark's Avatar
    Yesterday, 20:41
    Looks good. -Dan
    2 replies | 28 view(s)
  • Euge's Avatar
    Yesterday, 12:39
    Euge replied to a thread 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 | 150 view(s)
  • Euge's Avatar
    Yesterday, 02:05
    Euge replied to a thread 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 | 150 view(s)
  • Euge's Avatar
    Yesterday, 01:53
    Euge replied to a thread 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 | 150 view(s)
  • Euge's Avatar
    Yesterday, 00:35
    Euge replied to a thread 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 | 150 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 | 163 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 | 82 view(s)
  • topsquark's Avatar
    March 25th, 2017, 21:31
    At a guess you are forgetting about the cross term. (a + b)^2 \neq a^2 + b^2. It is (a + b)^2 = a^2 + 2ab + b^2. You are going to end up having to...
    4 replies | 54 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 | 78 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 | 67 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 | 23 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 | 62 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 | 78 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 | 67 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 | 73 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 | 78 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 | 67 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 | 83 view(s)
  • topsquark's Avatar
    March 24th, 2017, 23:16
    topsquark replied to a thread Factoring...7 in Pre-Calculus
    I mentioned this in another thread. Don't set the LHS of "a = a + b" It's too confusing. -Dan
    3 replies | 48 view(s)
  • topsquark's Avatar
    March 24th, 2017, 23:13
    topsquark replied to a thread Factoring...6 in Pre-Calculus
    You need to clarify your variables. "b = (a - b)" isn't right. Pick a variable name, say, p... Anything but that b on the LHS.... Then you have p...
    5 replies | 73 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 | 78 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 | 67 view(s)
  • topsquark's Avatar
    March 24th, 2017, 21:05
    topsquark replied to a thread Factoring...5 in Pre-Calculus
    Yeppers! -Dan
    2 replies | 33 view(s)
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About Chris L T521

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