All Questions
Tagged with applications calculus
175
questions
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Software for Exportable NURBS surfaces from Parametric Equations $x=f(u, v), y=f(u, v), z=f(u, v)$ (Must be Suitable for Engineering)
The title pretty much says it all. Is there any software out there that lets you input 3D parametric equations without having to go to the trouble of writing a bunch of code and then lets you export ...
- 11
1
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0
answers
79
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Using the trapezoidal rule for the Maxwell-Boltzman function
Background
I approached my physics professor with question 1 from this LibreTexts resource. (at the bottom of the page), to better understand the material via self-study.
Question
Using the Maxwell-...
- 1,426
28
votes
4
answers
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Consider a man who travelled exactly 2 km in two hours. Is there a one-hour interval when he traveled exactly 1 km?
Question :
Consider a man who travelled exactly 2 km in two hours.
Is there a one-hour interval when he traveled exactly 1 km?
Can we make a mathematical argument?
I have written my attempt in an ...
- 3,227
4
votes
6
answers
693
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Is $x^3$ really an increasing function for all intervals?
I had an argument with my maths teacher today...
He says, along with another classmate of mine that $x^3$ is increasing for all intervals. I argue that it isn't.
If we look at conditions for ...
- 45
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46
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What are applications of changing limit and differentiation/integration?
I know the following theorems but don’t know their usefulness.
If a series $\{f_n\}$ of Riemann integrable functions on $[a, b]$ uniformly converges to $f$, $f$ is Riemann integrable and $\lim\limits_{...
- 103
1
vote
1
answer
91
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The absurdity of $\Gamma(x)$'s minimum, and can it be applied to the factorial?
I know that the Gamma function can be used as a representation of the factorial, but, at the same time, it is an extrapolation of $x!$. The Gamma function is cool and all, but what are its ...
- 751
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21
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Calculating Rate of Change and using differentials to project 3 years from now
Currently, BC is helping $R=5,000$ refugees. The number of refugees that BC must help is rising at a rate of $\frac{dR}{dt}=1,000$ refugees per year. Currently, the number of staff members is $N=100$ ...
- 785
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1
answer
72
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Linear and almost linear Partial differential equations examples in Sciences
I am interested in learning linear and almost linear PDEs of first order to describe some system or process however I want to learn by real world examples of such a application.Do you know any such ...
- 121
2
votes
2
answers
98
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What is an actual application problem (probability, weather) that uses the binomial series? Does it solve anything?
I'm just trying to figure out what the purpose is of the binomial series? What does it tell us? I did a search and found something talking about probability and weather predicting, but I'd like to see ...
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1
answer
270
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Two questions re. the calculation of total mass in a rod of non-uniform density
I am currently learning about applying integration techniques to the calculation of mass in a rod of varying density. I feel as if I understand the general picture, but I have some specific points of ...
- 418
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0
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41
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Sequence of Logic in Diffusion Problem DQ
Problem: If a tank is filled with 100 gallons of water and mistakenly added 300 pounds of salt. To fix the mistake the brine is drained at 3 gallons per minute and replaced with water at the same rate....
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0
answers
45
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Cavalieri's Principle in volume calculation
In petroleum engineering, for easier calculation of the volume underlying a specific surface underground, the irregular surfaces are modeled by an equivalent surface with circular cross sections, ...
0
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0
answers
70
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Arc length vs Surface of revolution.
I don't understand why these two problems are solved differently here the first one $fig(1)$ and 2nd one $fig(2)$. Why did we take the limit $\displaystyle \lim_{r\to0^+}\int_r^\pi \sqrt{2-2cost}\...
user1062191
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1
answer
63
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Why can we apply the surface area of revolution theorem to a spiral?
To find the surface area generated by revolving function f which is smooth on the interval [a,b] and $f(y) \ge0$ around the y-axis we can use the formula $$S=\int_a^b 2\pi rdl =\int_a^b 2\pi f(y)\...
- 318
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2
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538
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When can I apply the trapezoidal rule?
An artificial lake has the shape illustrated below , with adjacent measurements 20 feet apart. Use suitable numerical method to estimate the surface area of the lake.
I know how to solve this problem ...
- 318
1
vote
1
answer
61
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Why can we say here that $\Delta x_i=dx$ as $i$ approaches infinity?
In the proof of the arc length formula we assume that an element of the arc length is $$\Delta L_i=\sqrt{(\Delta x_i)^2+(\Delta y_i)^2}=\sqrt{1+\left(\frac{\Delta y_i}{\Delta x_i}\right)^2}\space \...
user1062191
1
vote
1
answer
50
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Calculus application question
My attempt:
Step 1: Find $x$ in terms of $t$.
$\frac{dt}{dx} = \frac{1}{-0.15x}$
$t = \frac{1}{-0.15}\ln(x) = x^{-1}(t)$
$x(t) = e^{-0.15t}+c$
However, here is where I am stuck. Without any extra ...
- 1,190
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votes
1
answer
55
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Using an expression and an equation to get an ODE to describe something.
I have an expression and an equation, that I need to use to show that ODE describes something.
Let me put it into context
I have an expression for the Rate at Anti-Freeze flows $\mathcal{IN}$
and $\...
1
vote
1
answer
294
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Question in population dynamics using exponential growth rate equation
Given population doubles in 20 minutes, what is intrinsic growth rate r?
Attempt: Given population doubles, using exponential growth rate we have $\frac{dN}{dt}=2N$ so $N(t)=N_0e^{2t}$ therefore r=2, ...
- 395
3
votes
3
answers
573
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Why does the sign in Newton's method matter?
Deriving Newtons Method visually as with the help of a right triangle and assuming $x_1$ lies the left of $x_0$ we get $$x_1 = x_0 - \frac{f(x_0)}{f'(x_0)}$$
Using slope over run.
but if we assume $...
- 675
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1
answer
372
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What is the advantage of using Gradian to measure an angle?
What is the advantage of Gradian to measure an angle? For example, I know radian is useful in Calculus because e.g. it simplifies the derivative of trigonometric functions.
By the way, except the ...
- 225
4
votes
1
answer
387
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I've never been so confused (Application of Integral Calculus)
Here's a problem on Application of Integral calculus to find the work done in moving a particle. I was able to 'reach' the 'right answer'. But I'm totally confused and utterly dissatisfied with the ...
- 1,156
0
votes
2
answers
2k
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Work on a chain (applications of the integral)
A 10-foot-long chain weighs 25 lbs. And hangs from a ceiling. Calculate the work done in raising the lower end of the chain to the ceiling so that it is at the same level as the upper end.
Please, ...
0
votes
1
answer
100
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Calculus applications - oil leaking from a boat
So here is the question:
The fuel from a ship leaks into the sea forming a circular oil slick. The area of this circle is increasing at the rate of $20$ $m^2$ per minute.
They asked me to prove that ...
- 1,190
0
votes
1
answer
195
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Are limits as incredibly cool as I think they are?
I recently did all the limit maths, but I didn't put much thought into its significance. I thought, okay, it's perfectly reasonable to say that, for example, as $x\to 1$, $(\frac{x^2-1}{x-1})\to2$. ...
- 3,186
0
votes
1
answer
476
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Using 3D Piecewise Functions to Model a Rollercoaster
I am designing a roller coaster using functions (ie. linear, cubic, logarithmic, trigonometric). At some point, one of the parts of the rollercoaster does not follow a two dimensional graph, but ...
- 649
3
votes
1
answer
368
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Applications of matrix differentiation
I know that ordinary differentiation has many real world applications, from quantum physics to economics, but I cannot think of any real world applications of matrix differentiation. So, do any real ...
- 780
3
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2
answers
295
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Can we clarify this "accumulated money flow" application of integration?
I read about this model/application in Calculus with Applications, 11th Edition by Lial, Greenwell, and Ritchey (example), where if you have a function $f(t)$ that models some revenue stream, the rate ...
- 19k
1
vote
2
answers
402
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What uses does the product log function have?
I've been looking into complex functions and how to plot them in programing languages like Python and JavaScript. I still am wondering how to do stuff with complex functions like in my previous ...
user930105
0
votes
1
answer
396
views
Modelling interest with differential equations (IVP)
Problem : you set a bank account, with initial value k, the bank will pay you continuous interest of 12% per year.
a) write an initial value problem for your account balance y(t) after t years
Sol:
$$...
- 69
0
votes
1
answer
263
views
Mathematical expression for physical forces in pendulum ODE
A 16 lb weight is suspended from a spring having a spring constant of 5 lb/ft. Assume that an external force given by
24 sin (10t) and a damping force with damping constant 4, are acting on the spring....
- 612
1
vote
1
answer
425
views
Finding the formula for T from Newton's Law of Cooling
I think I got a wrong answer because I skipped a particular step which seemed optional. I'm still not too sure what happened though and would appreciate your help...
Background:
Newton’s law of ...
- 13
0
votes
1
answer
320
views
Calculus - Calculate Work done to lift water out of tank
I need help setting up the integral so that I can calculate the work done. I've tried it many times and have referred to Youtube, slader, the textbook, and also this site, but I still don't get how to ...
- 133
1
vote
0
answers
34
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Concerning some calculations for the elements in $(W^{1,2} (\Omega))^\prime$
The following question is motivated from the fact that I need to do some calculations in the weak sense, since I do not have enough regularity of the function $u$.
Let $ u \in L^2 (0,T; W^{1,2} (\...
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-3
votes
1
answer
83
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set up an integral when the following functions revolve around the $x$, $y$ and $y=\frac{1}{2}$ [closed]
$y=\sin x$, $y=\frac{1}{2}$, $x=0$
i got the same integral which is
$$
\int_0^{ \frac{5 \pi}{6}} \pi \left(\sin^2(x)- \frac{1}{4}\right) \, \mathrm d x.
$$
Anyone help
- 107
0
votes
0
answers
380
views
What are the real life application of absolute function?
The well-known absolute function $|x|$ has many uses in mathematics, physics, etc. I know one of the majority applications of abs function in the alternative current making with diodes. But it is ...
- 25.2k
0
votes
1
answer
105
views
Why is integration used so widely though they are just approximation?
Integration is used so widely in higher areas like rocket science etc. As integration is just approximation, even $0.01$ Pascal pressure error might bring a large disaster right! Even fuel consumption ...
- 3
0
votes
1
answer
109
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Help with volume integration application problem using Disk or Washer Methods, revolving about x-axis, revolving about y-axis.
I need to find the volumes of the solids generated by revolving the regions bounded by the graphs of the equations about the given lines: y = $\sqrt {x}$ $y=0$, and $x=3$. A) the $x-axis$ B) the $y-...
- 1
1
vote
0
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381
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Finding surface area element of a right oblique cone in polar coordinates using integration
I have this right angled oblique cone whose vertex is right angled with the diameter $2R$ and has a height $h$. I need to find the surface area element $dS$ for this cone. I know about the surface ...
0
votes
1
answer
2k
views
Moment of inertia of a cone frustum with a cylinder cut out (using integral)
How can I find moment of inertia of this frustum when the mass M is uniformly distributed through the grey region using integration?
The hints said to break the region into two pieces, one with ...
1
vote
1
answer
686
views
what is the volume generated by rotating the given region.
My professor says the volume generated by rotating the region $\mathscr{R}_2$ about the line $OA$ is $5/\pi$ but I don't see how that could be the answer?
- 107
2
votes
2
answers
225
views
Volume of a circle $x^2 +y^2 \leq 1$ which is revolving around a line $x+y=2$.
I want to compute the volume of a circle $x^2 +y^2 \leq 1$ which is revolving around a line $x+y=2$. Usually I solved problems about solids revolving around axis and non axis horizontal and vertical ...
0
votes
1
answer
342
views
Let $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$ be a differentiable function such that $\mathrm{f}(0)=0........$
Question: Let $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$ be a differentiable function such that $\mathrm{f}(0)=0, \mathrm{f}(1)=1$ and $\left|\mathrm{f}^{\prime}(\mathrm{x})\right|<2 \forall \...
- 323
2
votes
1
answer
165
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Area and Volumes of revolution using disc method
(1) The disk method to determine the volume of revolution uses the volume of a cylinder of width dx
a proof of this involves showing cylinders (disks) above the curve and those below the curve
...
- 21
1
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0
answers
49
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Physical significance of 3rd derivative [duplicate]
I am new to calculus and currently learning differentiation. I understood that the first derivative indicates the slope of the function and the second derivative indicates the rate at which the slope ...
- 647
-1
votes
1
answer
103
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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}$$
Does anybody ...
- 1
1
vote
1
answer
90
views
Why $\int_0^h 2 \pi \frac{rx}{h} \, dx \neq \pi rl$
I'm new to calculus.
I saw a proof for volume of cone using integral. They taken the cone's vertex at $(0,0,0)$, it's base centre at $(h,0,0)$ and it's radius is $r$
$$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