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• 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)
• 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 28th, 2020, 20:13
You also have an arithmetic error. When $\displaystyle t = 5$ you end up with $\displaystyle 5 = C - \frac{3}{121} \implies C = 5 + \frac{3}{121} =... 4 replies | 108 view(s) • March 28th, 2020, 18:48 Thanks for pointing out my error Hallsofivy. Adam is one of my students, and the topic they are learning is Laplace Transforms, so he will have to... 4 replies | 108 view(s) • March 28th, 2020, 05:02 Take the Laplace Transform of the equation:$\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 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, 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, 01:11 Prove It replied to a thread 2.6.5 implicit in Calculus What you've done is correct. 1 replies | 55 view(s) • March 24th, 2020, 23:51 Taking the Laplace Transform of the equation gives\displaystyle \begin{align*} s^2\,Y\left( s \right) - s\,y\left( 0 \right) - y'\left( 0...
0 replies | 56 view(s)
• March 24th, 2020, 23:26
This requires the convolution theorem: $\displaystyle \int_0^t{f\left( u \right) \,g\left( t- u \right) \,\mathrm{d}u } = F\left( s \right)... 0 replies | 62 view(s) • March 24th, 2020, 23:03 Start by taking the Laplace Transform of both equations, which gives$\displaystyle \begin{cases} s\,X\left( s \right) - s\,x\left( 0 \right) +...
0 replies | 49 view(s)
• March 23rd, 2020, 05:39
Prove It replied to a thread Intersection in Geometry
Start by replacing x with -5 + 8t, y with 1 + 10t, and z with 9 + 8t, in your plane.
1 replies | 128 view(s)
• March 23rd, 2020, 04:29
Prove It replied to a thread Laplace Convolution in Analysis
$\displaystyle \mathcal{L} \left\{ f\left( t \right) \right\} = F\left( s \right)$, so \displaystyle \begin{align*} \mathcal{L} \left\{ f\left(... 1 replies | 194 view(s) • March 23rd, 2020, 04:25 Actually it's\displaystyle \frac{9}{s^2 + 81} $. Actually it's$\displaystyle -\frac{3}{s - 9} + \frac{81}{s^2 + 81}$. To enter it in... 2 replies | 227 view(s) • March 23rd, 2020, 04:19 Hi Dean, this is Hayden, I'm assuming that you want to do a Laplace Transform of this. In future please post the ENTIRE question. I also expect it... 2 replies | 160 view(s) • March 23rd, 2020, 04:15 Try mathcal{T}, which gives$\displaystyle \mathcal{T}$. 2 replies | 96 view(s) • March 22nd, 2020, 20:08 The Heaviside function suggests a second shift, but to do that, the entire function needs to be a function of$\displaystyle t - 4$. Let... 0 replies | 82 view(s) • March 20th, 2020, 19:44 topsquark replied to a thread [SOLVED] s8.2.5.7 chain rule in Calculus Look at your first factor: \left ( 7x^6 + 8 x^3 \right ) ^3 = ( x^3 ( 7 x^3 + 8 ) )^3 = (x^3)^3 (7 x^3 + 8 )^3 Don't worry. It's an easy mistake... 2 replies | 279 view(s) • March 16th, 2020, 02:09$\displaystyle \begin{align*} \mathcal{L} \left\{ 5\sin{ \left( 11\,t \right) } \sinh{ \left( 11\,t \right) } \right\} &= \mathcal{L} \left\{...
0 replies | 114 view(s)
• March 14th, 2020, 23:06
All of the other answers could be true but since f(x) is not given we could make the function do some or all of these possibilities, as well as...
7 replies | 232 view(s)
• March 14th, 2020, 19:06
I'm just saying that f(x) can be anything so I had fun sketching it. -Dan
7 replies | 232 view(s)
• March 14th, 2020, 19:04
Just to round out the thread I (finally) have an explanation of 3) from my original post. (It looks worse than it is.) p^{ \mu } p^{ \nu } \to ...
7 replies | 683 view(s)
• March 14th, 2020, 17:50
Since we aren't given any real information about f(x) we need to be general. It's possible that f(x) can be just about anywhere is this interval. ...
7 replies | 232 view(s)
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1. Hello and welcome back to MHB, Prove It!

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2. Hello and welcome back to MHB, Prove It!

We are happy to see that you have returned, and we look forward to your continued participation here!

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3. Many thanks for your wonderful help!
4. Hey Prove It! Regarding this post, I think you mean $2-e$ is definitely incorrect, right? Since the function is positive in the given interval. Just wanted to give a heads-up.

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Fantini.
5. Hey , I noticed that you like solving integration problems. I think that your solutions are excellent and neat. Keep going !
6. Hi Prove It! I just want you to know that I split your thread Miko's question via email into two posts, so that it won't be shown up in the unanswered thread list. When bringing questions from other sites, please make sure you post the question in one post and the answer in another so that it wouldn't be shown up as an unanswered thread.
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