• Today, 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 | 59 view(s)
• Yesterday, 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 | 36 view(s)
• Yesterday, 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 | 59 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 | 250 view(s)
• March 30th, 2020, 04:26
Yep. (Nod) And no, nothing more specific.
21 replies | 250 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 | 58 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 | 250 view(s)
• March 29th, 2020, 14:38
Indeed. (Thinking)
21 replies | 250 view(s)
• March 29th, 2020, 14:26
Yep. (Nod)
21 replies | 250 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 | 250 view(s)
• March 29th, 2020, 13:19
That is a possibility yes. What happens if $f'(y)$ is negative? (Wondering)
21 replies | 250 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 | 250 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 | 250 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 | 250 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 | 250 view(s)
• March 28th, 2020, 20:13
You also have an arithmetic error. When $\displaystyle t = 5$ you end up with $\displaystyle 5 = C - \frac{3}{121} \implies C = 5 + \frac{3}{121} =... 4 replies | 108 view(s) • March 28th, 2020, 18:48 Thanks for pointing out my error Hallsofivy. Adam is one of my students, and the topic they are learning is Laplace Transforms, so he will have to... 4 replies | 108 view(s) • March 28th, 2020, 16:11 Welcome to the forum! I guess that "between" is supposed to mean "among", but I am not sure about "even". If it means "at least", then the... 2 replies | 201 view(s) • March 28th, 2020, 05:02 Take the Laplace Transform of the equation:$\displaystyle \begin{align*} s\,Y\left( s \right) - y\left( 0 \right) + 11\,Y\left( s \right) &=...
4 replies | 108 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 | 121 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 | 75 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 | 196 view(s)
• March 26th, 2020, 21:28
Prove It replied to a thread 3.2.15 mvt in Calculus
It's fine, well done.
3 replies | 121 view(s)
• March 26th, 2020, 21:23
Easy, $\displaystyle 0 \leq \sum{\frac{1}{5^{n-1} + 1}} < \sum{\frac{1}{5^{n-1}}} = \sum{ \left( \frac{1}{5} \right) ^{n-1} }$ Since your...
2 replies | 64 view(s)
• March 26th, 2020, 21:12
I am reading Tej Bahadur Singh: Elements of Topology, CRC Press, 2013 ... ... and am currently focused on Chapter 1, Section 1.4: Basis ... ......
0 replies | 91 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 | 64 view(s)
• March 26th, 2020, 20:17
Upon taking the Laplace Transform of the equation we have \$\displaystyle \begin{align*} s^2\,Y\left( s \right) - s\,y\left( 0 \right) - y'\left( 0...
0 replies | 58 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 | 58 view(s)
• March 26th, 2020, 14:09
Nice... (Smirk) Thank you very much!!! (Blush)
12 replies | 296 view(s)
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