• 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)
• 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 | 41 view(s)
• 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)
• 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 | 41 view(s)
• Yesterday, 21:25
Euge replied to a thread Ball Application in Pre-Calculus
Yes. Yes.
2 replies | 25 view(s)
• Yesterday, 21:19
Euge replied to a thread Find All Real Solutions in Pre-Calculus
Yes, it's correct.
2 replies | 36 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 | 150 view(s)
• Yesterday, 20:41
Looks good. -Dan
2 replies | 28 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 | 150 view(s)
• Yesterday, 02:53
you can apply either way. but next steps become simpler if you apply difference of square $x^6-y^6= (x^3+y^3)(x^3-y^3)$ 1st term is sum of cubes...
4 replies | 56 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 | 150 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 $n \ge... 12 replies | 150 view(s) • Yesterday, 00:35 Euge replied to a thread Real Analysis in Analysis Hi joypav, You're not bothering us with your questions, so feel free to ask whenever you have trouble. :) 12 replies | 150 view(s) • March 25th, 2017, 23:17 Yes. Let$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 | 163 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 | 82 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 | 54 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 | 78 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 | 67 view(s)
• March 25th, 2017, 20:52
Rewrite as $\sqrt{2t+5}+\sqrt{2t+8}=\sqrt{8t+25}$. What do you get when you square both sides?
4 replies | 54 view(s)
• 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)
• 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)
• 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)
• 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)
• 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 | 78 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 | 67 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 | 83 view(s)
• March 24th, 2017, 23:17
greg1313 replied to a thread Factoring...8 in Pre-Calculus
1. Correct. 2. Correct. 3. Yes, apply the sum of cubes formula to $8a^3+27b^3$. Be careful with your variable names. $a$ does not necessarily...
2 replies | 39 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)
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