All Questions
Tagged with applications calculus
175
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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
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1
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425
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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
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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
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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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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
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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 ...
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105
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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 ...
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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-...
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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 ...
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2k
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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
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1
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686
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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
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2
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225
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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 ...
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342
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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
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1
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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
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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 ...
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