All Questions
13
questions
28
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4
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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
0
votes
0
answers
70
views
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
0
votes
1
answer
63
views
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 $$S=\int_a^b 2\pi rdl =\int_a^b 2\pi f(y)\...
- 318
1
vote
1
answer
61
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Why can we say here that $\Delta x_i=dx$ as $i$ approaches infinity?
In the proof of the arc length formula we assume that an element of the arc length is $$\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
320
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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
0
votes
0
answers
380
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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
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
2
answers
195
views
One train travels north at $140$ mph towards Traveler's Town, while a second train travels west at $150$ mph away from Traveler's Town.
One train travels north at $140$ mph towards Traveler's Town, while a second train travels west at $150$ mph away from Traveler's Town. At time $t=0$, the first train is $70$ miles south and the ...
- 485
0
votes
1
answer
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Related Rates (Shadows)
Let me first apologize for what must be the $\frac{1}{\epsilon}$ th related rates question on this site, but I really have no idea how to tackle this. From Keisler's "Elementary Calculus":
Problem 3....
- 123
4
votes
3
answers
12k
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Real world situation with System of Equation with 3 variables?
Where do you run into a real world situation involving 3 variables and 3 equations? Can someone think of a specific example from business, etc? I recall taking an operations research course that ...
- 4,771
5
votes
7
answers
78k
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Application of Composition of Functions: Real world examples?
Do you know of a real world example where you'd combine two functions into a composite function? I see this topic in Algebra 2 textbooks, but rarely see actual applications of it. It's usually plug ...
- 4,771
27
votes
9
answers
148k
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What is a simple example of a limit in the real world?
This morning, I read Wikipedia's informal definition of a limit:
Informally, a function f assigns an output $f(x)$ to every input $x$. The
function has a limit $L$ at an input $p$ if $f(x)$ is "...
- 3,426