I have the following function
$$f^{(0)}\left(x\right)=f\left(x\right)=e^{x}$$
And want to approximate it using Taylor at the point ##\frac{1}{\sqrt e} ##
I also want to decide (without calculator)whether the error in the approximation is smaller than ##\frac{1}{25} ##
The Taylor polynomial is...
I'm trying to find the local truncation error of the autonomous ODE: fx/ft = f(x).
I know that the error is |x(t1) − x1|, but I can't successfully figure out the Taylor expansion to get to the answer, which I believe is O(h^3).
Any help would be greatly appreciated!
x = fraction of potentiometer connected to load
Vp in parrallel with VL = x/(Rp/RL.x.(1-x) + 1)
If RL = infinite, then Ro = x and Vo = x.Vs
If RL = finite, then Ro = x/(Rp/RL.x.(1-x) + 1) and Vo = x.Vs/(Rp/RL.x.(1-x) + 1)
Therefore error is x.Vs - x.Vs/(Rp/RL.x.(1-x) + 1)
Trying to break the...
NOTE: this is a programming exercise (Python).
I started adding to ##x_{true}## an error related to a (for example) 10% relative error, obtaining ##x_{measurement}##. Then i computed ##y_{measurement}##. To find the precision, i calculated ##(y_{true}-y_{measurement})/y_{measurement}##. If it is...
In "The Theoretical Minimum" (the one on classical mechanics), on page 218, the authors write a Lagrangian
$$L=\frac m 2 (\dot r^2 +r^2\dot \theta ^2)+\frac {GMm} r$$
They then apply the Euler-Lagrange equation ##\frac d {dt}\frac {dL} {d\dot r}=\frac {dL} {dr}## (I know there should be...
I know I am posting this in the wrong sub-forum, but I am unable to enter certain sub-forums (and when I login I just get a "security" error), where as in other sub-forums I am automatically logged in. Is there a problem with the site or just me experiencing these problems?
Homework Statement
(b)
A nuclear research reactor produces radiation for neutron scattering measurements. A safety procedure shuts the reactor down if a radiation level monitoring detector measures more than 3 counts per minute. In a test, 156 counts are recorded during a random 24 hour...
Homework Statement
2) A student is performing an angry bird experiment in real life. He calculates the range of the projectile by shooting the bird with a 30 degree angle and an initial velocity of v0 = 20 m/s.
a) If the relative accuracy of setting the projectile angle is delta theta/theta =...
There is something I seriously don't understand about uncertainty.
Suppose there is an electric balance that reads 5.67g
The limit of reading is 0.01g
The greatest possible error is half of the limit of reading and is thus 0.005g
By this logic, and assuming the very best possible situation, I...
Hello everyone, I'm trying to solve a BVP that seems to be very sensitive, for which I have to provide a starting guess and hope the program can fix it to find a solution. The program has been tested many times and it is very solid, the only problem should be that I can't find the right guess...
Homework Statement
A string (m = 1 kg) fixed at both ends is vibrating in its second harmonic mode. If the length of the string is 2 m and it feels 50 N of tension, which of the following is NOT a possible harmonic frequency for this string?
a) 1.25 Hz
b) 2.5 Hz
c) 5 Hz
d) 10 Hz
e) 20 Hz...
Homework Statement
[/B]
I was reviewing this stuff and although I excelled at it once, I seem to forget some of it.
For example, please consider this:
Homework Equations
R_C=\frac {R_1R_2} {R_1+R_2} + R_3
Here's the correct formula for its error:
\Delta R_C=\frac {R_1R_2} {R_1+R_2} \left[...
Sorry for two questions in a row, this one we have been stumped on for the entire day
We're getting "fatal error. detector no. 1 of tally 5 is not in any cell.", What could be causing this?
In the manual and all examples we've seen, nobody has parameters specifying cell location for the...
Homework Statement
I have the following integral I wish to solve (preferably analytically):
$$ I(x,t) = \int_{-\infty}^{0} \exp{[-(\sigma^2 + i\frac{t}{2})p^2 + (2\sigma ^2 p_a + ix)p]} \ dp$$
where ##x## ranges from ##-\infty## to ##\infty## and ##t## from ##0## to ##\infty##. ##\sigma##...
Homework Statement
I have an empty cylinder with an external diameter of (23.0 ± 0.5) mm, an internal diameter of (22.5 ± 0.5) mm and a height of (60.0 ± 0.5) mm. I need to calculate its volume with its uncertainty/error.
Homework Equations
The Attempt at a Solution
I do it like this...
Hello,
I am trying to find a Magnetostatic(3D) solution for my design. My design consist of a coil embedded in Ceramic material developed by LTCC technology. I am below queries:
1. Is it important to define a material"Insulating"? How it will affect the Inductance of the system and the...
There is solid empirical evidence that error in particle physics measurements is not actually distributed in a Guassian manner. Why don't particle physicists routinely use student t error distributions with fat tails that fit the reality of errors in experimental measurement more accurately...
Homework Statement
I have the following integral,
$$\frac{1}{\sigma \sqrt{2\pi} t} \int_{-\infty}^{0} \exp[\frac{-1}{2\sigma ^2} (\frac{x-x_0}{t} - p_0)^2]dx$$
that I wish to write in terms of the error function,
$$erf(x) = \frac{2}{\sqrt{\pi}} \int_{0}^{x} e^{-g^2}dg$$
However, I can't seem...
My question is simple, and I'm only asking it because most places talk about more advanced problems than this one:
I've measured the radius of a sphere (a very regular one) with a micrometer of 0.01 mm resolution.
I took 3 measures (rotating it between each measure), and all of them were...
Anyone recognise this problem?
When looking at posts with (presumably) Latex formulae, I get [Math Processing Error] instead of the formula.
It looks like everyone else can read them ok and even stranger, I sometimes see the formula for a brief moment before it is replaced by the message...
Hey, I'm trying to propagate my percentage errors through some hefty equations and come up on a bit of snag:
I've got a percentage error for x and know how to deal with it for trig functions and powers, however since both errors are from the same source:
y = sin(x)^2 / x^2
Should I just...
So I am doing the charge to mass experiment and determining the relationship between:
1. accelerating voltage and radius formed by the electron beam
2. magnetic field strength and radius formed by electron beam
Theoretically I should obtain an equation of the form:
r = (1/B) *sqrt(2mV/e)
where...
I'm trying to use Maxima to examine the error in a Fourier series as the number of terms increases. I've figured out how to produce a Fourier series and plot partial sums, but this has me stumped.
If anyone experienced with the Maxima CAS has some insight into this, I would greatly appreciate...
Homework Statement
In textbook i was given formula to calculate error.
I know that:
E(t) = f(t)- L(x) = f(t) - f(a)- f'(a)(t- a) [L(x) is linear approximation]; [Lets call this Formula 1]
I understand that, but that I have formula:
E(x) = f''(s)/2 * (x-a)^2 [lets call this Formula 2]
Here...
During a lab exercise we measured different masses of a magnetic material on a scale while changing the strength of the magnetic field it was in. Afterwards we plotted the masses and the fieldstrength hoping to find a linear slope. Then we drew a linear slope by using linear regression and found...
During a labexercise we measured a value to be 26.3 mT. The teslameter was said to have an accuracy at +- 0.05%. This means we measured 26.3 +- 0.0132mT. However we are supposed to write a measured value with it's error in the last digit. But the error is smaller than the smallest digit we got...
HI Guys,
I am getting an error in Ansys Maxwell that says
Maxwell2d solver, process solver2d: Internal Solver Error: 'In the Material: M270-35A_12 , the SLOPE of the End Two Points in this BH curve is 56519.1, which is more than 2 times of Mu0; This may lead to a non-physical solution...
Homework Statement
Run a transient simulation and plot the three outputs, Vo(t), on the same plot. Use the following settings:
1. Set the Run Time (or Stop Time) so that you plot 3 cycles of Vo(t).
2. Set the Maximum Step Size so that you get at least 100 points per period for Vo(t).
3. Set...