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• 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 | 39 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 | 85 view(s)
• March 31st, 2020, 17:53
Wait! What do you mean by you changed it to v(t)? The particle's position is x(t) = sin(t) - cos(t) means that v = \dfrac{dx}{dt}. You can't just...
2 replies | 50 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 | 85 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, 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, 07:38
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 27th, 2020, 23:42
Here is this week's POTW: ----- Find the minimum value of $(u-v)^2+\left(\sqrt{2-u^2}-\dfrac{9}{v}\right)^2$ for $0<u<\sqrt{2}$ and $v>0$. ...
0 replies | 82 view(s)
• March 27th, 2020, 23:38
Hi MHB! I have decided to extend the deadline by another week so that our members can give this problem another shot and I am looking forward to...
1 replies | 202 view(s)
• March 26th, 2020, 20:42
Have you tried looking at \lim_{n \to \infty} \dfrac{a_{n + 1}}{a_n}? -Dan
2 replies | 71 view(s)
• March 26th, 2020, 18:35
Let y'(x) = v(x). Then your equation becomes v'(x) + v(x) = -F(x) Now you have a first degree linear ordinary differential equation. You can't...
1 replies | 64 view(s)
• March 25th, 2020, 17:42
Yep. (Nod) I'd say 'and this is confirmed...' rather than 'since this is confimed...' though. (Emo)
12 replies | 327 view(s)
• March 25th, 2020, 15:50
Ah good. (Whew) Does the solution for $x$ match the given general solution? (Wondering)
12 replies | 327 view(s)
• March 25th, 2020, 15:40
How did you get $x_{1}=\frac{1}{3}$? (Wondering)
12 replies | 327 view(s)
• March 25th, 2020, 15:06
Don't we have $x_2=h(y)$ so that $f(x_2)=f(h(y))=y$? And therefore $g(f(x_2))=g(y)=x_1$? (Wondering)
4 replies | 115 view(s)
• March 25th, 2020, 14:35
Suppose it is correct, then what are the solutions of $Ax=\begin{bmatrix}1\\3\end{bmatrix}$? (Thinking)
12 replies | 327 view(s)
• March 25th, 2020, 14:33
Hey mathmari!! How about a proof by contradiction? That is, suppose $g\not\equiv h$, then there must be an $y\in B$ such that $g(y)\ne h(y)$,...
4 replies | 115 view(s)
• March 25th, 2020, 14:13
Since we should get the same $A$ regardless of the value of $\lambda$, I think that for instance $a_{12}$ must be $0$. (Thinking)
12 replies | 327 view(s)
• March 24th, 2020, 15:20
Hey evinda!! $A$ is a fixed matrix, isn't it? It shouldn't depend on $\lambda$ should it? (Worried) The lambda is only supposed to describe...
12 replies | 327 view(s)
• March 23rd, 2020, 06:48
Well, to be fair, this is not immediately obvious. (Worried) Let's take a slightly different angle. According to the wiki page about matrix...
3 replies | 183 view(s)
• March 23rd, 2020, 03:44
Hi Peter, Capital Tau is just a T. Mathjax doesn't have a caligraphic Tau, but the caligraphic T is the same thing: $\mathcal{T(S)}$....
2 replies | 102 view(s)
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