What is Test: Definition and 1000 Discussions

So we have the theorem: if ##a_n>0## and ##\lim_{n\to \infty} a_{n+1}/a_n = L## then ##\lim_{n\to \infty} a_n^{1/n}=L##. Now, the proof that I had seen for ##L\ne0## that we choose ##\epsilon<L##. But what about the case of ##\epsilon>L##, in which case we have: ##a_{n+1}>(L-\epsilon)a_n## but...

Homework Statement Use the integral test to compare the series to an appropriate improper integral, then use a comparison test to show the integral converges or diverges and conclude whether the initial series converges or diverges. ##\sum_{n=3}^\infty \frac{n^2+3}{n^{5/2}+n^2+n+1}## Homework...

According to wikipedia, this is how to calculate flexural stress where "the loading span is 1/3 of the support span (rectangular cross section)": stress = force x length / (width x (depth x depth)) Stress ("outer fibers at midpoint"), (MPa) Force ("load at a given point on the load deflection...

If anyone side of a triangle cannot be derived from Euclid’s formula for pythagorean triples, is this sufficient to prove that a right triangle with integer sides is impossible? For example, let's take the leg expressed by k2mn in Euclid's formula,, where k,m,n, are integers. If one of the...

Homework Statement If Z(X,Y) = (X^2+Y^2)*(P(X) + Q(Y)), how to convert it to one-factor-at-a-time test matrix ? Write down the relevant formula and give a brief explanation. Homework Equations below: in my attempt The Attempt at a Solution Z(X1,X4) =P(X1)*Q(X4)...

Hello. I am doing problem sets on very basic stat topics. When solving problems that require the use of chi-squared table, I stumbled upon an unexpected issue. I seem to miss something important about how to correctly choose the right critical value using the chi-squared table. Below are two...

Homework Statement Use the integral test to determine whether $$\sum_{n=3}^{\infty} \frac{1}{n^2-4}$$ converges or diverges.The Attempt at a Solution [/B] Taking the integral we have $$\int_{}^{\infty}\frac{dn}{n^2-4}$$ Note: Mary Baos text is having us write the integrals without lower bounds...

Given a test charge, let's say on the vertical y axis. Another charge vertically below it moves past at a significant speed compared to c. From the Lorentz transformations (in most E&M books) the electric field and thus the force on the test charge will be greater than would be the static...

We have been testing a Cummins VTA-1710-G2 Diesel Generator 1800 RPM 480 Vac 671 kW with an Avtron K580 load bank that is hooked up to our three 480 Vac output cables and one cable to our facility ground. The generator output breaker keeps tripping when the load is around 350 kW. The test...

Hello, I was given f(-4x)= 1/(1+4x), and I used the geometric series to find the power series representation of this function. I then took the limit of (-4x)^k by using ratio test. The answer is abs. value of x. So -1/4<x<1/4 I then plugged in those end points to the series going from k=0 to...

Homework Statement Use the integral test to show that the sum of the series gif.latex ##\sum_{n=1}^\infty \dfrac{1}{1+n^2}## is smaller than pi/2. Homework EquationsThe Attempt at a Solution I know that the series converges, and the integral converges to pi/4. As far as I´ve understood...

Hi guys! Here's a problem i was working on. I solved it by root test and got absolute value of x on the outside of the limit and the limit equaled zero. Is it wrong to multiply the outside absolute value by the zero I got from the limit? or is that okay? In general, when we are solving power...

Homework Statement LiCl flame test is red. a) define what process b)and transition between which energy levels?2. The attempt at a solution a)I believe that the process would be emission, as photons are emitted when energy is released b)n=2 to n=1 I assumed that that would be the lowest energy...

Hi, I read a research paper for verification and validation of solidity code. It uses F* (F-star). However, it has to convert the solidity code into F-star. I can't find the converter. Can some body please guide me how to manually test the code? Code is given below: contract MyBank {...

Homework Statement If you had a solution of Magnesium carbonate, what results would you expect from the following four tests: Precipitation Test, Flame Test, Benedicts Reagents Test, Dilute Acid Test. Could someone take a look at my reasoning to how the Magnesium Carbonate would react under...

If ##f'(0) = 0## and ##n## is the smallest natural number such that ##f^{(n)}(0)\neq 0##, then the higher-order derivative test states the following: 1. If ##n## is even and ##f^{(n)}(0)>0##, then ##f## has a local minimum at ##0##. 2. If ##n## is even and ##f^{(n)}(0)<0##, then ##f## has a...

The DTT project proposal talks about a D-D reaction inside the future tokamak that is going to be built in Italy, Frascati. Which is the reason of this choise? The cross section is smaller than the D-T reaction one, and neutrons are less energetic. How this influences heat and particle exhaust...

I would like to disconnect the secondary windings from a stereo preamp to test the voltages of the secondary windings. The transformer has a 330 - 0 - 330 volt center tapped secondary and a 10.9 volt secondary. It is to be used with house current - 110 or so in Virginia. I have measured the...

In order to do some welding a long way from a power socket, I have made up a 200m long ‘extension lead’ from some 6mm2 armour cable. The cable is needed for another job later on. I have an test unit that: 1. Checks earth/ground bond with 8Vac and 25A. 2. Then measures insulation resistance...

All, Through work, I've recently been tasked with investigating a very old tensile test technique, according to BS HC 403:1977 (now withdrawn). Essentially, you take a ring. Anywhere along it you make a slit all the way through. You then pull that ring in a tensile machine, ensuring that the...

Hello there. I'm a veteran science teacher at the middle and high school level. I've taught a few years of physics and am interested in moving towards engineering. I have looked at a number of available curricula like Project Lead the Way which require a significant investment in time and money...

Hi If I know the velocity, mass and diameter of a missile from a failed pressure test how can I calculate the minimum thickness of a containment sheet steel wall say 1 meter away?

Hi, during my driving lesson today my road test instructor said that he says that he feels comfortable with me on the road test this time. This will be my second attempt at the road test and my 5 hour class is next sunday.

Spec My job, as an undergraduate EE student, is to create a test rig for offsite electronics (environmental sensors hooked up to a data logger, 12V batteries and solar panels). The test rig should be able to evaluate output from sensors (serial TTL, analog voltage, 1-wire) and output required...

I'm simplifying a research question that I have at work. Assuming I have 2 coins each with a different probability of head, let's call heads a success (p). Those are biased coins each with a different p, and I do not know the probability of success of each coin, but I do got a sample: Coin 1 -...

This snip off is from Himedia Widal test teaching kit. I understand 1/20 1/40 1/80... are the concentrations in each test tube. They are obtained by the following calculation: (2nd testube) 1/2 X 1/20. But I can't decipher the numbers written at the top, 10-1 , 10-2 etc. Besides which of of...

I know that there exists non-geometrical proofs that the usual mapping of the Klein Bottle in ##\mathbb{R}^3## is an immersion. But I would like to see an actual geometrical 'test'. I was thinking if saying that on the self intersection, which I circled in red below, the map being injective can...

Hi All I made an experiment where I measured the change of the impedance of a coil when I changed a environment parameter X times. For each change I collected ~20 samples. So I have a table with X lines that represent the number the change of the parameter and 20 columns that represent the...

I don't think this is related to linear dependence/independence of linear algebra. I am talking about multi-variable calculus. I am getting confused with being able to quickly tell which variables depend on others when there are 4+ variables involved. For example, suppose I have w(r,s)...

Homework Statement in tests to choose the most comfortable shock absorbents, 3 cars are used, with the same mass "m", and the same springs, but different shock absorbents. the graphs show the changes in car height when passing over a bump (y=0 being the normal state of the car). . . . -Witch...

So I finished my first year of college and I'll be transferring to a new college where a C or better is required. However my Intro to Anthropology(100) class I had an absolutely terrible professor who gave me a C- and so now it won't transfer and I'm out of $1,400. So my question is am I able...

Homework Statement >Which of the following aqueous solutions would test closet to 7 on the pH scale? $a) NaCl$, $b) Na_2CO_3$, $c) NaH_2PO_4$, $d) NaCN$ Homework EquationsThe Attempt at a Solution I don't understand this. So I tried writing chemical equations like for a), NaCl + H20 --> NaOH +...

Not sure if this reference has been posted yet, but I just saw it come through and thought I'd share. This is the "Big Bell Test Collaboration" using measurement choices provided by persons (as opposed to computer generated "random" choices). (The authors are a virtual who's who in the world...

Hi, Just curious. One of the requirements for a data set to be normally-distributed is that of symmetry. Question: Is there or could one define a statistic to this effect, meaning to determine the level of symmetry on the data set and use that to determine at certain confidence level if the...

I am a contractor. I install water lines. Once installed we have to pressure test them. We pump the lines up to 150 PSI of water. If the PSI drops one of 2 things is wrong, either i have a leak in the line, or there is a small amount of air in the line. Generally if it is air, it stabilizes...

I'm looking at the proof of the alternating series test, and the basic idea is that the odd and even partial sums converge to the same number, and that this implies that the series converges as a whole. What I don't understand is why the even and odd partial sums converging to the same limit...

Homework Statement Homework EquationsThe Attempt at a Solution So the book is saying that this series diverges, i have learned my lesson and have stopped doubting the authors of this book but i don't understand how this series diverges. ok i can use the comparison test using 1/3n and 1/3n...

Homework Statement I need to design a pressure test that, in one cycle, will simulate the 8000 cycles that a given pressure vessel will undergo. I know the dimensions and material of the vessel, the number of pressure cycles it will undergo, and the max and min working pressures. Homework...

Hi, I'm currently working on a project for which I have to determine the Life-Time of a certain mechanical component within a certain confidence interval. By sampling a small number (let's say n = 10) of these components and measuring the number of hours until failure, I want to determine this...

i want to be able to test the ph of foods and drinks so I purchesed a digital ph tester for water. Is there a better ph tester option ? If I wanted to test the ph of something like mayonnaise would I just stick the tester into the mayo or would I need to mix the mayo with water first?

In a left-tailed test, the value of the test statistic is -2. If we know the shaded area is 0.03, then we have sufficient evidence to reject the null hypothesis at 0.05 level of significance.

Hey! :o A public transport company claims that its buses are at least $95\%$ on time. (A bus is still on time here, if he has at most $3$ minutes delay compared to the timetable.) A sample size of $n = 1000$ at various stops results in $66$ delays. The probability that a randomly selected bus...

I would like to compare four slopes I got from linear fits through five data points for each fit. The fitting results (for the slopes) are as follows: 1: 0.08885 ± 0.00991 2: 0.08744 ± 0.0118 3: 0.10288 ± 0.00669 4: 0.0926 ± 0.01285 My hypothesis is that they are all not significantly different...

Setting up a test stand that will need a controller to cycles a device ON and OFF at an adjustable time interval (allows me to make the ON duration and OFF duration whatever I want). It will also need to keep a count, so I can track the cycles count and also set a limit on cycles so it will stop...

I was wondering about contact resistance measurment test. Why do we take such test?

The problem In this problem I am supposed to show that the following series converges by somehow comparing it to ## \frac{1}{k\sqrt{k}} ## : $$ \sum^{\infty}_{k=1} \left( \frac{1}{\sqrt{k}} - \frac{1}{\sqrt{k+1}} \right) $$ The attempt ## \frac{1}{\sqrt{k}} - \frac{1}{\sqrt{k+1}} =...

As we draw the electric field lines due to 2 equal magnitude and same nature charges. But when we solve the question concerning the same case we take the resultant of forces due to both charges at a test charge in such a manner that the 2nd charge(let I put the test charge on the left side i.e...

Gravity is weak - while we can study the other interactions with individual particles, for gravity we need macroscopic objects to get measurable forces. This makes it easy to measure quantum effects for the other interactions, but hard to do so with gravity. Gravitational forces are always...

Hi all, I have done the question in two methods. The first method is done by rational root test and the second method is by modulo p (theorem is as attached). It seems that my answers for both methods do not tally. 1. Where have I done wrong in the attached for the methods? Which is the...

Homework Statement A planet has a gaseous atmosphere with a density of 0.1 g/cm³. The planet itself completely consists of liquid methane with a density of 0.4 g/cm³ and has a radius of 3800 km. A test balloon is dropped onto this planet, which consists of a helium spherical balloon (1 m³, mass...