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• Today, 17:02
Prove It is not giving you the answer he is giving you a suggestion that you can use the limit he posted. See if there is any kind of substitution...
4 replies | 48 view(s)
• Today, 12:06
Hi all, I think even we do switch to XF (is still going to happen) the time has come to make a change. We have a database of amazing content here...
0 replies | 38 view(s)
• Today, 11:37
Hi all, I hope you are all safe, healthy, and not affected in a serious way by the world wide COVID-19 virus. Here in the US it has completely...
0 replies | 23 view(s)
• Today, 11:34
Hey mathmari!! This is an example where Newton-Raphson can have problems if we are not careful. If we pick a starting value that is too far from...
2 replies | 33 view(s)
• Today, 10:30
\frac{\left(x\sin\left(\pi\left(x-1\right)\right)\right)}{e^{x/9}(x-1)} The above graph shows that the function repeats its value at $x=1$ when $x$...
2 replies | 33 view(s)
• Yesterday, 10:37
I substituted $n=\frac 1{x^2}$, which also means that $x^2=\frac 1 n$. So we get $\Big(1 + \frac 32 x^2\Big)^{1/x^2} = \Big(1 + \frac 32 \cdot \frac... 7 replies | 150 view(s) • Yesterday, 09:14 It's like this: $$\Big(1-\frac 12 x^2 + \ldots\Big)\Big(1+\frac 12 (2x)^2 - \ldots\Big)\\ =1\cdot 1 -\frac 12 x^2 \cdot 1+1\cdot \frac 12 (2x)^2 -... 7 replies | 150 view(s) • Yesterday, 07:04 The series expansion of \cos x = 1 - \frac 12x^2 + \ldots. And the expansion of \frac 1{1-x} = 1+x+x^2+\ldots So:$$\frac{\cos(x)}{\cos(2x)}... 7 replies | 150 view(s) • Yesterday, 01:08 Here is this week's POTW: ----- Suppose that the positive integers$x, y$satisfy$2x^2+x=3y^2+y$. Show that$x-y, 2x+2y+1, 3x+3y+1$are all... 0 replies | 102 view(s) • Yesterday, 01:02 No one answered last week's POTW.(Sadface) Below is a suggested solution: The given function is the square of the distance between a point of the... 1 replies | 138 view(s) • April 4th, 2020, 04:14 This is actually a proof of (ii)$\Rightarrow$(iii) in Lemma 3.2. So we are assuming that (ii) holds. In particular, since$\overline{ f(A) }$is... 1 replies | 118 view(s) • April 3rd, 2020, 15:47 I have obtained access to the full solutions manual, after contacting Wiley about it. I will not type up the solution in full, but simply note a few... 1 replies | 170 view(s) • April 2nd, 2020, 15:47 In the mid-1990's, an electrical engineer/computer scientist by the name of Judea Pearl started to change the world by greatly improving our... 0 replies | 132 view(s) • April 2nd, 2020, 12:25 Klaas van Aarsen replied to a thread f in Calculus It appears the answer is: dkm Acronym for "don't kill me". Often used when somebody says something that somebody else finds really funny,... 5 replies | 220 view(s) • April 2nd, 2020, 11:56 topsquark replied to a thread f in Calculus I believe the proper question is "What the 'f'?" -Dan 5 replies | 220 view(s) • April 1st, 2020, 15:04$\newcommand{\doop}{\operatorname{do}}$Problem: (This is from Study question 4.3.1 from Causal Inference in Statistics: A Primer, by Pearl,... 1 replies | 170 view(s) • April 1st, 2020, 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 | 208 view(s) • March 31st, 2020, 17:53 topsquark replied to a thread [SOLVED] 299What is the acceleration in Calculus 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... 4 replies | 191 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 | 208 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 | 437 view(s) • March 30th, 2020, 04:26 Yep. (Nod) And no, nothing more specific. 21 replies | 437 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 | 437 view(s) • March 29th, 2020, 14:38 Indeed. (Thinking) 21 replies | 437 view(s) • March 29th, 2020, 14:26 Yep. (Nod) 21 replies | 437 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 | 437 view(s)
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