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• Today, 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 | 63 view(s)
• 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 | 162 view(s)
• Yesterday, 22:32
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 | 58 view(s)
• Yesterday, 21:35
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 | 58 view(s)
• Yesterday, 21:25
Euge replied to a thread Ball Application in Pre-Calculus
Yes. Yes.
2 replies | 31 view(s)
• Yesterday, 21:19
Euge replied to a thread Find All Real Solutions in Pre-Calculus
Yes, it's correct.
2 replies | 44 view(s)
• 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 | 162 view(s)
• Yesterday, 20:41
Looks good. -Dan
2 replies | 32 view(s)
• 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 | 162 view(s)
• Yesterday, 11:46
Rido12 replied to a thread copper(2) oxide in Other Topics
There are many exceptions. I remember back in my first year chemistry course, my professor criticized the textbook for providing incorrect...
5 replies | 76 view(s)
• 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 | 162 view(s)
• 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 $n \ge... 12 replies | 162 view(s) • Yesterday, 00:35 Euge replied to a thread Real Analysis in Analysis Hi joypav, You're not bothering us with your questions, so feel free to ask whenever you have trouble. :) 12 replies | 162 view(s) • March 25th, 2017, 23:17 Yes. Let$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 | 170 view(s)
• 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 | 84 view(s)
• 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 | 56 view(s)
• 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 | 84 view(s)
• 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 | 72 view(s)
• 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 | 84 view(s)
• 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 | 72 view(s)
• 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)
• 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 | 84 view(s)
• 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 | 72 view(s)
• 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 | 84 view(s)
• 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)
• 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)
• 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 | 84 view(s)
• 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 | 72 view(s)
• March 24th, 2017, 21:05
topsquark replied to a thread Factoring...5 in Pre-Calculus
Yeppers! -Dan
2 replies | 33 view(s)
• March 24th, 2017, 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...
7 replies | 170 view(s)
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### 16 Visitor Messages

1. Hi Deveno ... ... Hope you return to MHBs soon ... you are sadly missed ...

Peter
2. Hi Deveno ... haven't seen you for a while ... hope all is well with you ...

Best regards,

Peter
3. Hi Deveno,

work has taken me out of the state of Tasmania and into regional Victoria ... about 150kms outside Melbourne ...

Should re-establish broadband links and get some time in a day or so ...

Thanks as always for you help ...

Peter
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anemone.
5. Good answers on Peter's questions, and well-given exercises too. Unfortunately though I wouldn't be able to check Peter's work on the matrix algebras. Every ring is commutative to me
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7. Hello, David, what d'you think of the group theoretic analogy of galois theory I have posted in the abstract algebra forum? Can this thing be arrow-theoretically generalized to categories too?
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