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
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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 ...
0
votes
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, ...
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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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votes
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 $$S=\int_a^b 2\pi rdl =\int_a^b 2\pi f(y)\...
- 318
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2
answers
538
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When can I apply the trapezoidal rule?
An artificial lake has the shape illustrated below , with adjacent measurements 20 feet apart. Use suitable numerical method to estimate the surface area of the lake.
I know how to solve this problem ...
- 318
1
vote
1
answer
61
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Why can we say here that $\Delta x_i=dx$ as $i$ approaches infinity?
In the proof of the arc length formula we assume that an element of the arc length is $$\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
0
votes
1
answer
55
views
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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votes
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
views
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
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2
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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
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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:
$$...
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