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• Today, 11:21
HallsofIvy replied to a thread f in Calculus
??what??
2 replies | 29 view(s)
• Yesterday, 15:04
$\newcommand{\doop}{\operatorname{do}}$ Problem: (This is from Study question 4.3.1 from Causal Inference in Statistics: A Primer, by Pearl,...
0 replies | 40 view(s)
• Yesterday, 08:33
The Bisection Method is used to solve equations of the form $\displaystyle f\left( x \right) = 0$, so we need to rewrite the equation as...
0 replies | 38 view(s)
• Yesterday, 07:44
You first have to write this DE as a system of first order equations. Note, since $\displaystyle t$ does not appear in the original DE, that means...
0 replies | 35 view(s)
• Yesterday, 07:35
HallsofIvy replied to a thread Cathode and Anode in Chemistry
You can blame Benjamin Franklin and others of that time! When initially studying static electricity and the way it moves from one place to anther...
2 replies | 299 view(s)
• Yesterday, 06:35
Not quite, although you started correctly. The limit in this case is as $x\to\infty$, so you want to see what happens when $x$ gets large. This means...
3 replies | 87 view(s)
• March 31st, 2020, 14:52
Hi Goody, and welcome to MHB! To prove that \lim_{x\to\infty}\frac{x-1}{x+2} = 1, you have to show that, given $\varepsilon > 0$, you can find $N$...
3 replies | 87 view(s)
• March 30th, 2020, 05:31
Let's take a look at a couple of examples. If $f(x)=x$, then $f'(x)=1$ and $f''(x)=0$. So $\lim\limits_{x\to +\infty}f'(x)\ne 0$, isn't it?...
21 replies | 294 view(s)
• March 30th, 2020, 04:26
Yep. (Nod) And no, nothing more specific.
21 replies | 294 view(s)
• March 30th, 2020, 04:23
Prove It replied to a thread 34 mnt in Calculus
The average acceleration is $\displaystyle \frac{20}{\frac{1}{6}} = 120 \,\textrm{mi}/\textrm{h}^2$ Since the function is continuous and smooth,...
1 replies | 75 view(s)
• March 30th, 2020, 03:32
I believe so yes. Consider $f(x)=\ell$. It satisfies all conditions, doesn't it? (Wondering) And it is monotone instead of strictly monotone. To...
21 replies | 294 view(s)
• March 29th, 2020, 14:38
Indeed. (Thinking)
21 replies | 294 view(s)
• March 29th, 2020, 14:26
Yep. (Nod)
21 replies | 294 view(s)
• March 29th, 2020, 13:57
Then the inequality also holds yes. What if fill in, say, $f'(y)=-1$ in the inequality? Would it satisfy it? (Wondering)
21 replies | 294 view(s)
• March 29th, 2020, 13:19
That is a possibility yes. What happens if $f'(y)$ is negative? (Wondering)
21 replies | 294 view(s)
• March 29th, 2020, 13:08
We have an expression with $f(y)$, $f'(y)$, and $\ell$. And we already know that $\ell\in\mathbb R$, don't we? So it can't be $\pm\infty$ either. ...
21 replies | 294 view(s)
• March 29th, 2020, 10:27
Ah okay. But that is not the case now is it? (Wondering) Sounds like a plan. (Nod)
21 replies | 294 view(s)
• March 29th, 2020, 08:35
Let's see, suppose we pick a convex function, say $f(x)=x^2$. It's convex isn't it? Does $\lim\limits_{x\to +\infty}f'(x)$ exist? (Wondering) ...
21 replies | 294 view(s)
• March 29th, 2020, 07:48
Isn't "x^2*2016x" the same as "2016x^3"?
2 replies | 140 view(s)
• March 29th, 2020, 07:41
Argh! Arithmetic! I never was any good at that!
4 replies | 111 view(s)
• March 29th, 2020, 07:38
Hey mathmari!! Let's start with: It follows from $\lim\limits_{x\rightarrow +\infty}f(x)=\ell$ that $\lim\limits_{x\to +\infty}f'(x)=0$...
21 replies | 294 view(s)
• March 28th, 2020, 20:13
You also have an arithmetic error. When $\displaystyle t = 5$ you end up with $\displaystyle 5 = C - \frac{3}{121} \implies C = 5 + \frac{3}{121} =... 4 replies | 111 view(s) • March 28th, 2020, 18:48 Thanks for pointing out my error Hallsofivy. Adam is one of my students, and the topic they are learning is Laplace Transforms, so he will have to... 4 replies | 111 view(s) • March 28th, 2020, 16:11 Welcome to the forum! I guess that "between" is supposed to mean "among", but I am not sure about "even". If it means "at least", then the... 2 replies | 209 view(s) • March 28th, 2020, 08:15 Let me, yet again, state my dislike for the "Laplace Transform Method"! And, in fact, Prove It made a slight arithmetic error (easy to do with... 4 replies | 111 view(s) • March 28th, 2020, 05:02 Take the Laplace Transform of the equation:$\displaystyle \begin{align*} s\,Y\left( s \right) - y\left( 0 \right) + 11\,Y\left( s \right) &=...
4 replies | 111 view(s)
• March 28th, 2020, 04:42
Prove It replied to a thread 3.2.15 mvt in Calculus
I think the OP just means they are not sure if this is considered the most concise or elegant way, or if there are any steps that are not...
3 replies | 137 view(s)
• March 27th, 2020, 13:51
What language was this originally in? Things like "There is even one student between these boys" make no sense at all to me! What is the...
2 replies | 209 view(s)
• March 27th, 2020, 13:13
So $x^2+ y= z^2$ for x, y, and z integers. That is the same as $x^2- z^2= (x- z)(x+ z)= y$. Look at the ways to factor y: y= mn and the x- z= m, x+...
1 replies | 106 view(s)
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### 25 Visitor Messages

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2. Thanks Fantini
3. Haha. \widehat's cool. Also check out \widetilde. But these sometimes get ugly.
4. Yep. Corrected now.
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