What is Test: Definition and 1000 Discussions

Hello. How do I find the limit of this term? $$\lim_{{n}\to{\infty}}|\left(\frac{n}{n+1}\right)^{\!{n^2}}|^\frac{1}{n}$$ This is the working but I don't understand how to get the third line. r = lim(n→∞) |[n/(n+1)]^(n^2)|^(1/n) ..= lim(n→∞) [n/(n+1)]^n ..= lim(n→∞) 1 / [(n+1)/n]^n...

Hello. How do I find the limit of this term? $$\lim_{{n}\to{\infty}}|\left(\frac{n}{n+1}\right)^{\!{n^2}}|^\frac{1}{n}$$

This technically might not belong here, mods, put it in it's proper place if not. So I'm studying for a test on Monday. Not a big deal, we use webassign, you may commence with the horrified gasps and groans, I know. So here's my odd little situation. I get a problem like this one Integral...

Hello. How do I determine whether to use ratio test or root test in determining whether a series is convergent or divergant? For example, in this problem, ratio is used for no.1 and root test for no.2. Why is that? I need explanation, please.

Hello. How do I determine whether to use ratio test or root test in determining whether a series is convergent or divergant? For example, in this problem, ratio is used for no.1 and root test for no.2. Why is that? I need explanation, please.

Just a few quick questions this time: I'm doubting the first one mostly, because when I used the integral test to evaluate it: I ended up getting (-1/x)(lnx +1) from 2 to infinity, which gave me an odd expression: (-1/infinity)(infinity +1 -ln2 -1). I'm assuming this means it is convergent...

I need to test the ph of river. I need a method of making an indicator that I can make at home. Please help !

Hello, Given the complex linear mapping: T(z) = Az + B where A is real and B is complex. However trying to show that T(a * z1 + z2) = a * T(z1) + T(z2) does not work which implies the mapping is not linear? Why does not this rule apply here? Thanks.

I am doing critical points and using the second derivative test (multivariable version) Homework Statement f(x,y) = (x^2+y^2)e^{x^2-y^2} Issue I am having is with the system of equations to get the critical points from partial wrt x, wrt y The Attempt at a Solution f_{x} =...

Hi All, I am trying too undestand the slit test which shows wave-particle duality. Please correct me if I am wrong on the basic info on the test. One photon is shot out and if there is one slit it will go through the slit and make a point on the detection medium behind the slit. However if both...

VLSI testing is process that is used to determine that chip is good or faulty VLSI chip is tested by test equipment and some test circuit can anybody tell me the example of some test circuit actually I am confused I don't understand that fault model and test circuit are different or...

I have a pressure vessel of volume V= 1 m^3 . The atmospheric pressure Patm = 101 kPa and Tatm = 22 C. I slowly pump liquid water into the pressure vessel until the internal pressure reaches P1 = 15 MPa. Also, the process is isothermal because the water was pumped in slowly and heat is exchange...

Homework Statement Hey! So I just have a quick question. In my notes I wrote down that the alternating series test only proves absolute or conditional convergence, but can not prove divergence. Is this true or did I misunderstand my professor? Homework Equations The Attempt at a...

Homework Statement Hello, I am working on problems 6-14 on the attached PDF. Don't be scared off, they are just one line of code each. I got number 6 correct, and I got partial credit on 7 and 8, but I am trying to figure out why it is not right. Homework Equations The Attempt at a...

I'm trying to find if this series converges or diverges using the comparison test: and the answer goes: My problem is, I am not sure how to go from 1/2^(n+1) to 1/2(1/2)^n. can you please explain that to me

This is not a homework problem. I'm doing it for fun. But it is the kind that might appear on homework. Homework Statement I'm trying to prove that if lim n→∞ |an+1/an| = L < 1, then \Sigma an converges absolutely and therefore converges. Homework Equations The Attempt at a Solution Here's...

Paired means test vs two-sample means test [solved] Hi. When it comes to hypothesis testing, what is the difference between the two-sample tests and the paired test? I know one difference is that you use the latter when the two variables are dependant and the former when they're...

A quiz has 4 questions with 3 choices for each answer. If you guess every answer, in how many different ways can you complete this test?__________ How many students must take this test to guarantee that at least 3 identical answer sheets are submitted?__________ I know how that the answer to...

Homework Statement See attached image. (it should say "ratio" not "ration") Homework Equations Ratio series test: An+1/An The Attempt at a Solution I have worked this problem over and over and continue to get the same solution. Some guy worked it on the board a couple of days ago and got...

I am in a zero mass spaceship at rest in my chosen frame of reference. A cylinder with a diameter equal to the sun and of infinite length is passing at 8 minutes light travel distance and has a velocity of 99% x the speed of light traveling with the length of the cylinder with respect to my...

Hello, I'm in need of major help on some equations.. I have an exam coming up for finals and I'm horrid at algebra in general. I'm in intermediate algebra for the second time. Soo.. yeah, help would be greatly appreciated. Thank you! (Please explain step by step.) 1. Rationalize the...

Homework Statement f(x,y) = x^{2}+y^{2}-2x, D is a closed triangular region with vertices (2,0) (0,2) and (0,-2). Find the absolute max and min of f on D. Homework Equations Hessian matrix. The Attempt at a Solution Taking the second partials I end up with the system of equations...

Is anyone pumped? Because I'm pumped and you should be pumped. GET PUMPED! My last chance to get a 2300, fingers crossed.

Homework Statement Use the comparison test to show that the series converges, and find the value it converge to by using partial fractions. ∑ n=1 -> ∞: \frac{2}{n^2 + 5n + 6} Homework Equations The Attempt at a Solution The series can be written as 2 * ∑ n=1 -> ∞...

For those who have made diagrams in TikZ 2.10, the previous version, atan2 has be redefined. Therefore, any code built off the old definition will compile but the output may not be what you expect. Before it was atan2(\x2-\x1, \y2-\y1). Now it is atan2(\y2-\y1, \x2-\x1). If you want to test...

Hi there! Im new to this forum so pardon me if this is the wrong place to post my question. Basically, I have an idea with regards to doing some modification to phone screens. However, there is no such technology (yet) for this and I have zero knowledge and background pertaining to...

Homework Statement I've found that the typical way for using ratio test is to find the limit of an+1/an However, my tutor said that radius of convergence can be found by finding the limit of an/an+1 and the x term is excluded. For example:Finding the interval of convergence of n!xn/nn my...

We manufacture crank case heaters and they are designed with an 800V 1A STD Recovery diode. We do not Hi-pot the heater with the diode in it we only test to make sure we have an ohm reading in one direction and an OL in the other. However, our customer installs our heater into a system and...

Homework Statement Evaluate ## ∑^∞_{n=1} \frac {2}{n(n+2)} ## 2. The attempt at a solution I've solved this question simply enough by evaluating it as a telescoping series and found the answer as 3/2. Now, when applying the integral test, it only works when dealing with positive, decreasing...

I'm studying using the popular Lindenberg book. It suggest I have to memorize about 30 elements and their respective oxidation numbers. However, the book was written before they revamped the exam. Anyone know if I still have to memorize this?

I have done a test on a 4 piston test engine which is expected to exhibit torsional resonance at 800RPM and a vertical translational resonance at 1200RPM. The data we gathered from the test bed machine was as follows: Theta | Signal 0 | -5 60 | -1 120 | 7 180...

Hello, it is well-known that the Chi-square test between an observed distribution O and an expected distribution E can be interpreted as a test based on (twice) the second order Taylor approximation of the Kullback-Leibler divergence, i.e.: 2\,\mathcal{D}_{KL}(O \| E) \approx \sum_i...

This is a problem from My book which I have hard understanding what they are asking for, I am pretty confused on the question would like to have help! Second derivate test works as follows: If f (c) = 0 and f'' (c)> 0 Then c is a local min point for function f (a) Show that c need not be a...

Suppose: \int^{\infty}_1 \frac{x}{x^2 + 1} \, dx I can't do this can I? Let u = x^2 + 1 so du = 2x \, dx \therefore \frac{du}{2} = x \, dx ?

I was taking a test yesterday and this question came up, it could possibly be the only one I missed on the test. I roughly sketched and described the problem to the best of my memory, but I guarantee that all of the essential information is there. I have attached the problem to this question...

Homework Statement "Is there sufficient evidence to support the claim that the mean content of all such containers is at least 3 litres? Homework Equations The Attempt at a Solution I'm not sure what H0 and H1 will be H0: The mean content is not at least 3L H1: The...

Hello, I have a 16x16 contingency table, and I would like to perform a test in order to reject the hypothesis of independence between the variable X (columns) and the other variable Y (rows). Unfortunately many cells in the table contain zeros. The zeros are due to the fact that the sample...

I work at a company that manufactures TPU screen filters for the mining industry. I've got a test to do to inspect whether the qaulity of the TPU is affected by time in the heated barrel of the injection moulding machine. The TPU material sits in the barrel due to tea and lunch breaks (15 - 30...

I've never done this before, and undertook it for the first time today, guided by books, google, and YouTube. My truck's a 4 cylinder. I did the first test after driving it for a while to warm it up. I got 150-150-146-140 psi for the four respective cylinders 1-2-3-4. The instruction I was...

Suppose ##f^{\prime\prime}## is continuous on an open interval that contains x = c 1. If ##f^{\prime}(c)=0## and ##f^{\prime\prime}(c)<0##, then ##f## has local maximum at x = c. 2. If ##f^{\prime}(c)=0## and ##f^{\prime\prime}(c)>0##, then ##f## has local minimum at x = c. 3. If...

I played around in another thread with mathematically determining where a car should be time wise on 1/4 mile run. I had a chance to drive this car myself giving me more information than you normally have on a car you have yet to buy. As I thought more deeply about my calculations, I became...

The graph of a differentiable function y=f(x) is 1. concave up on an interval I if f' is increasing on I. 2. concave down on an interval I if f' is decreasing on I. Let y=f(x) is twice differentiable on an interval I 1. If f'' > 0 on I, the graph of f over I is concave up. 2. If f'' <...

Homework Statement U= { (x1, x2, x3, x4) | x1 x3 ≥ -5 } The Attempt at a Solution Let x = (1,2,3,4) and y = (1,2,3,4) x+ y = (2,4,6,8) x1x3 = 2x6 = 12 12 >-5 so closure by addition is fulfilled. I've been hearing contradicting information-some state that any 1 test of...

I was completing a chapter on momentum in my physics textbook. I took the test, in which I encountered the following question: Would a cat without a tail be able to right itself while falling so that it always landed on its feet? Earlier in the chapter the author explained that cats were...

Homework Statement Test to see if \sum_{n=1}^{\infty}{ i^n/n } converges.Homework Equations See above. The Attempt at a Solution If I separate this series into real/imag. parts both series diverges by the integral test. However, according to Wolfram Alpha, the series converges to...

This might seem like a rudimentary question but when trying to prove divergence (or even convergence) of an infinite series does the series always have to start at n = 1? For example would doing a test for \sum^{∞}_{n=1}\frac{1}{n} be any different from \sum^{∞}_{n=0}\frac{1}{n}

Homework Statement A 50 KVA,6360 V/230 V transformer is tested on open and short-circuit to obtain its efficiency,the results being as follows: O.C.: Primary Voltage-6360 V, Primary Current-1 A, Power Input - 2 kW S.C: Voltage across primary winding-180 V Current in secondary...

Homework Statement ∞n=1∑(-1)n\stackrel{10n}{(n+1)!} Homework Equations The Attempt at a Solution I already found that the limit does equal zero by using the ratio test on bn. What I'm having trouble with is determining if it decreases or not. I know you can't take the derivative...

Hi all I am comparing the performance of two models and have calculated the coefficient of determination R squared for each. I would like however to test the significance of this value. The F test however requires that the number of degrees of freedom for each model. The trouble is one...

I am not sure if this is the right sub-forum to post this question in or not, if not I appologize for posting in the wrong place - it looked like the most likely forum to be the correct one. In a sci-fi book I was reading, the author talked about an 'artificial symbiote' being created by 15...