All Questions
Tagged with applications calculus
175
questions
-1
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1
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Calculating if Romeo and Juliet will stay together always or not. [closed]
I have two equations which describe the Love of Romeo for Juliet (R) and Love of Juliet for Romeo (J) as a function of time, $t$.
$R=-c_1e^{3t}-c_2e^{2t}$
$J=2c_1e^{3t}+c_2e^{2t}$
They will stay ...
- 25
0
votes
1
answer
170
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Inverse function in $\mathbb{R}^3$
i'm looking for an inverse function in a 3 dimensions space :
$f~:~[0,1]^3\to[0,1]^3$
$$f(x,y,z)=\begin{pmatrix}x(1-(y+z)/2+yz/3)\\y(1-(x+z)/2+xz/3)\\z(1-(y+x)/2+yx/3)\end{pmatrix}$$
Does anybody ...
- 1
1
vote
1
answer
90
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Why $\int_0^h 2 \pi \frac{rx}{h} \, dx \neq \pi rl$
I'm new to calculus.
I saw a proof for volume of cone using integral. They taken the cone's vertex at $(0,0,0)$, it's base centre at $(h,0,0)$ and it's radius is $r$
$$V=\int_0^h \pi \left(\frac{rx}{h}...
- 15
0
votes
1
answer
46
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Solving time derivative of glycogen dynamics: $17.6{dG\over dt} = 2000 - 13G^2$ [closed]
Can I find G, glycogen level at time t=5, if glycogen dynamics are described by the following derivative:
$$17.6{dG\over dt} = 2000 - 13G^2$$
It's been a long time since I've messed with derivatives ...
- 1
0
votes
0
answers
123
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How to decompose the given function into several peaked functions like Gaussian or Lorentzian?
During applied mathematics, I am wondering how to decompose the data $[x,y]$ into several elliptic-shaped functions, namely
$$f[x,y]= H \cdot \left( 1 + \bigl( \frac{x-x_1}{a_1} \bigr)^2 + \bigl( \...
- 95
0
votes
3
answers
84
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examples of cases showing that knowing the area under a curve really matters ( at the elementary level)
It is often said that integral calculus offers a means to solve the area problem. My question, simply aims at understanding what is the interest of this area problem ( at the most basic level).
...
user655689
1
vote
2
answers
5k
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What are some applications of linear approximation in the real world?
What are examples you can give to Calculus I high school students?
Here is a link to show the level linear approximations will be taught.
I've found some applications by a simple google search. ...
- 63
0
votes
1
answer
408
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Finding the maximum curvature
I am trying to find the maximum curvature of $y=1/x$. I know to begin, I find k(x), which is: $k(x) = \frac {2}{x^3 (1+1/x^2)^{3/2}}$. But I'm confused as to where to go from here.
- 1
0
votes
2
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88
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A calculus problem from high school textbook
A man 150 cm tall, walks away from a source of light situated at the top of a pole 5 m high at the rate of 0.7 m/s. Find the rate at which:
his shadow is lengthening
the tip of his shadow is moving
...
- 27
0
votes
1
answer
1k
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Given $a_0, a_1,....,a_n$ are the real numbers satisfying
Given $a_0, a_1, .., a_n$ are the real numbers satisfying
$$\dfrac {a_0}{n+1} + \dfrac {a_1}{n} +......+\dfrac {a_{n-1}}{2}+a_n=0$$
then prove that there exists at least one real root of the equation ...
- 7,426
5
votes
1
answer
3k
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Using Rolle's theorem to show $e^x=1+x$ has only one real root
Applying Rolle's Theorem, prove that the given equation has only one root:
$$e^x=1+x$$
By inspection, we can say that $x=0$ is one root of the equation. But how can we use Rolle's theorem to prove ...
- 7,426
0
votes
1
answer
72
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calculus applied to fields in physics
Having trouble with the maths in this question, I realise this is a physics question so I apologise if this isn't allowed, but some mathematicians might be able to solve it well. I asked this in the ...
- 29
2
votes
6
answers
2k
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Importance of differentiation [duplicate]
I have just started learning about differentiation. I know that differentiation is about finding the slopes of curves of functions and etc.
I have many saying that differential and integral calculus ...
- 2,060
0
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0
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130
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Understanding a function space
I was reading a paper on Homogenization theory, where the author uses the spaces of vector valued functions. Let us consider such a space $D[\Omega; C^\infty_P(Y)]$, consisting of all the compactly ...
- 155
1
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1
answer
253
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set up triple integral for volume
I was working on practice problems in the textbook and got stuck on this question. Any help would be greatly appreciated.
Set up two triple integrals with two different orders of integration that ...
- 21