Converging Definition and 178 Threads

So I have plotted all the given data points on a graph, putting 1/di on the y- axis and 1/do on the x-axis. I have to now find focal length from the graph? I'm not sure how, I'm thinking I have to rearrange the equation 1/f = 1/do + 1/di into y = mx + b form then go from there, but I'm totally...

Prove that the series $$\sum_{k = 1}^\infty \frac{(-1)^{k-1}}{|x| + k}$$ converges for all ##x\in \mathbb{R}## to a Lipschitz function on ##\mathbb{R}##.

I do not have any reasonable attempts at this problem, as I am trying to figure out how one can get the correct answer when we are not given any values. Maybe if some of you sees a mistake here, that implies that the values from the previous example should be used... ##a_3 = a_1 \cdot k{2}##...

Would somebody be kind enough to check whether I've picked the right convergence tests for each of these and reached the right answers? There are no solutions in the book. Also, is there a method I can use to determine if I'm right - does calculating the first n terms help? Thank you Edit...

A sequence is made up of two sequences an=(n^2)/(n+2) - (n^2)/(n+3) The problem asks for the solver to work out if it's converging or diverging, and find a limit if possible. My first thought was to write both over a common denominator and then divide through by the dominant term; this...

Summary:: I cannot seem to get the answer to the following question. For (a) I am using the formula 1/V= 1/U- 1/F, giving me 7.5cm. I am then adding this to 50cm to get 57.5cm. I then used -1/20-1/57.5-1/v to get **-14.9cm** which is Incorrect. Any help greatly appreciated!

For compressible flow in a duct, mass conservation combined with reversibility (no entropy change) implies $$(1-\frac{u^2}{c^2})\frac{du}{u} = -\frac{dA}{A}$$ where u is the flow velocity of the gas, c is the speed of sound in the gas, and A is the area of the duct. I am assuming a calorically...

I am aware that the object would be to the left of the lens and the image would be to the right, but I don't understand what it is mean by " A converging lens of focal length f = 8.96 cm forms a sharp image for two positions of the lens." I don't understand where the two positions would be and...

Let ##Q## - charge of one of conductor, ##\phi_1## --- potential of charged conductor, ##\phi_2## --- potential of uncharged conductor. For the charged conductor: \begin{equation} \phi_1 = D_{11}Q , \end{equation} for uncharged conductor: \begin{equation} \phi_2 = D_{21}Q \end{equation}

I have been struggling with a problem for a long time. I need to solve the second order partial differential equation $$\frac{1}{G_{zx}}\frac{\partial ^2\phi (x,y)}{\partial^2 y}+\frac{1}{G_{zy}}\frac{\partial ^2\phi (x,y)}{\partial^2 x}=-2 \theta$$ where ##G_{zy}##, ##G_{zx}##, ##\theta##...

I tried -M=pq = f/(f-p) = f/f - f/p = 1-(f/p) => M+1= -f/p => -Mp-p=f But since it’s the y intercept, p will equal zero and so the focal length will be 0?

There's a phenomenon over at Wikipedia. Namely, all or most (?) topics converge to "philosophy". Is there a name or some kind of coherent explanation for this phenomenon? Is it just simply the case that most branches of science originated from philosophy, and this is apparent in how Wikipedia...

Homework Statement [/B] Let ##S\subset \mathbb{R}## be nonempty and bounded above. Show that there must exist a sequence ##\{a_n\}_{n=1}^\infty\subseteq S## such that ##\lim_{n\to\infty}a_n=\sup(S)##. Homework EquationsThe Attempt at a Solution Here is my idea. Let ##\epsilon >0##. Then there...

I've made a drawing of what is confusing me here. 1. This should be a case of focusing into infinity or not? 2. Can anyone explain what happens with the owl?

If two objects are traveling on paths at 90 deg to each other such that they will converge at a point how do we describe that motion. For example 2 cars are approaching a 4 way intersection and will collide. They see each other as moving diagonally yet when they collide one will t-bone the...

In the textbook I have (its a textbook for calculus from my undergrad studies, written by Greek authors) some times it uses the lemma that "for any irrational number there exists a sequence of rational numbers that converges to it", and it doesn't have a proof for it, just saying that it is a...

Homework Statement [/B] What is directly given in the problem: Converging lens with f=1.43m Hi = 2m Homework Equations Hi/Ho = di/do M = Hi/Ho = di/do 1/f = 1/do + 1/di The Attempt at a Solution Ho = 2m * 20 = 40m Not sure how I can get do from this. All of the equations seem to need di.

Howdy all, I'm looking at having two (preferably) stainless steel rods inside a plastic tube (for insulation and so they don't touch) with a push spring inside and between the two rods pushing each other away from one another, when not activated inside of an electromagnetic coil. When the coil...

Homework Statement Homework Equations I'm not sure any, perhaps 1/v + 1/u = 1/f The Attempt at a Solution [/B] I knowp enlargened real images will only be produced if the object distance is lower than the image distance, so that rules out B. Similarly I know that enlargened virtual images...

Homework Statement You are required to set up a light source, an object grid, a converging lens and a screen so that a quantitative investigation of object and image distances can be performed. Tabulate corresponding object and image distances (p and p' respectively). Also tabulate values of...

So, here's the problem I've come up with that I wanted to solve. We're going to be using a polar coordinate system for this one. A will represent our angle theta, and r will represent our radial coordinate. We are going to be looking at a non-compressible Newtonian viscous fluids. I'll now put...

Hello. Today I used a magnifying glass and observed how it converged sun light to a smaller area. The smaller the area and the more violet was the light diffused by the surface. Why does this happen? Then I used a mirror hoping the small violet point would be reflected, but it didn't happen...

Homework Statement Homework Equations \frac{1}{p}+\frac{1}{q}=\frac{1}{f} The Attempt at a Solution I already had this typed in word so here is a screen shot: I don't understand why the negative is omitted in the "correct answer" "B." In solving this problem I wanted to proceed in...

Homework Statement " A converging lens has a focal length f. The object location at magnification equal to -1 is? " Homework Equations m = -S'/S The Attempt at a Solution Here is my solution: M= -1 , S=?? M= -S'/S -1 = -S'/S S= -S'/-1 S=S' And from case 2 that says if an object is placed...

Homework Statement . Three thin lenses, each with a focal length of 40.0 cm, are aligned on a common axis; adjacent lenses are separated by 52.0 cm. Find the position of the image of a small object on the axis, 80.0 cm to the left of the first lens. d=52cm between f=40cm d of object=80cm...

Homework Statement A thin converging lens has radii of curvature of R1=9cm and R2=-11cm. Assume its focal points F1 and F2 are 5cm from the center of the lens. Determine its index of refraction. Homework Equations Len's Makers equation: 1/f = (n2 - n1 / n1) (1/R1 - 1/R2) The Attempt at a...

Mod note: Moved from Homework section I know that ##1/n^4## converges because of comparison test with ##1/n^2## (larger series) converges . how do I know ##1/n^2## converges? coz I cannot compare it with ##1/n## harmonic series as it diverges. @REVIANNA, if you post in the Homework & Coursework...

Homework Statement A real object is put in-between a convex lens (f = 30.0cm) and a plane mirror as shown in the figure below. Two images of the object are observed : a real image 50.0cm to the left of the lens and a virtual image to the right of the lens. The size of the virtual image is 3.00...

Homework Statement A microscope slide is placed in front of a converging lens with a focal length of 2.44 cm. The lens forms an image of the slide 12.9 cm from the slide. a. How far is the lens from the slide if the image is real? Homework Equations 1/f = 1/di + 1/do The real equation (but...

Homework Statement A magnifying glass has a converging lens of focal length 15.0 cm. At what distance from a nickel should you hold this lens to get an image with a magnification of +2.00? Homework Equations 1/f = 1/di + 1/do m = -di/do or hi/ho The Attempt at a Solution I tried to set it up...

Homework Statement An outdoor security camera has a simple lens with focal object length fo = 6.00 cm and perfectly focuses the image of a bird onto its detector located 9.00 cm away from the lens. The animal then flies away from the lens and the new focal distance is 8.00 cm. (a) How far did...

Homework Statement Given a sequence (x_n), x_n > 0 for every n\in\mathbb{N} and \lim\limits_{n\to\infty} x_n = L > 0, show that \ln x_n\to \ln L when n\to\infty. Homework EquationsThe Attempt at a Solution As logarithm function is an elementary function, meaning it is continuous in its domain...

Homework Statement All the necessary data is in the code, I'm just trying to converge NR, I decided to use the equation S = V^2 / Z since I had the admittance matrix and powers (needed voltages) I think my simple algorithm has a slight issue I can't find. Homework Equations Thank you! The...

e is the limit of an exponential of a number that is approaching one. The exponential makes it want to blow up, but the closeness to 1 keeps that in check. It's really a remarkable number! My question is, how easy is it to find ways to converge to arbitrary numbers other then e? Almost every...

Hello, I'm looking for some help with this problem for my Calculus 2 class. Since it's a summer class my professor wasn't able to explain everything fully so if you can help me that would be great : ) 1. Homework Statement Select the FIRST correct reason why the given series converges. A...

Homework Statement A converging meniscus lens is made of glass with index of refraction n = 1.55, and its sides have radii of curvature of 4.5 cm and 9 cm. The concave surface is placed upward and filled with carbon tetrachloride which has index of refraction n' = 1.46. Using the result in...

Hey everyone. So I just experimented on compressible flow through a converging diverging nozzle. The nozzle had 8 pressure points from where which pressure was measured, as well as inlet and outlet pressures. The inlet pressure and mass flow rate were adjusted to form subsonic flow and adjusted...

1. I am supposed to create a device that can intensify the light directed at a light intensity sensor. A small light bulb will be 25 cm away from the light sensor. My device is required to be 20cm long and placed in between the light bulb and the light sensor in order to make the light that is...

Homework Statement air flows through a device such that the stagnation pressure is 0.6 MPa, the stagnation temperature is 400° C, and the velocy is 570 m/s. Determine the static pressure and temperature of the air at this state. Homework Equations Tt=T + V2 / 2 Cp where Cp is 1.005 Kj/ Kg* °...

Hi. A spherical wave ##e^{i(kr-\omega t)}## diverging from a single point ##(x=0,y=0,z=-z_0)## can be approximated as a parabolic wave in the paraxial case around the z-axis. I.e., ##k r = k \sqrt{x^2+y^2+z^2} \simeq k (z +\frac{x^2+y^2}{2z})##. OK, then let's say a lens is placed such that its...

Homework Statement A)Find the final position of the image (from the object, I assume?) B)Find the size of the final image of the object. Homework Equations 1/f = 1/do + 1/di The Attempt at a Solution 1) Solved first distance: 1/5 - 1/4 = 1/di --> 4/20 - 5/20, di = -20cm 2) Use di1 for do...

Homework Statement Image: http://i.imgur.com/NMS7BUK.jpg?1 a) Find the position of the final image of the 1.0-cm-tall object. b) Find the size of the final image of the 1.0-cm-tall object. h = 1 cm f1 = 5 cm do = 4 cm f2 = -8 cm L = 12 cm di = ? Homework Equations 1/f = 1/do + 1/diThe...

Homework Statement A thin converging lens made of glass (##n_g=1.55##) happens to have an inclusion of water (##n_w=1.33##) at the center. The lens surfaces have radii of curvature ##R_{out} = r_1=r_2=10m##, and the water inclusion has the shape of a diverging lens with radii of curvature...

I could really use some help on this problem as well! Thanks!

Homework Statement A diverging lens (f = –13.0 cm) is located 18.0 cm to the left of a converging lens (f = 31.0 cm). A 3.30-cm-tall object stands to the left of the diverging lens, exactly at its focal point. Determine the distance of the final image relative to the converging lens Homework...

Homework Statement A converging meniscus lens is made of glass with index of refraction n = 1.55, and its sides have radii of curvature of 4.5 cm and 9 cm. The concave surface is placed upward and filled with carbon tetrachloride which has index of refraction n' = 1.46. Determine the focal...

Does all the light entering our eyes converge to a single point on the retina (assuming minimal aberration)? If this is true then that means that only a tiny point is exposed to light inside the eye so it will hit and activate a single cell (unless the cells are much smaller than the point of...

Homework Statement A small object is located on some distance from a converging lens. At some distant behind a converging lens lies a flat mirror. The resulting image is exactly at the same location as the small object. Why can we deduce that the object is located in the focal point of the...

I hope this is the right place to ask this. It is an experiment question. I have a 785 nm laser and a 1550 nm laser and I need to converge them down to a point. Now I could just manually align the lasers on the same XY-plane and have them hit that spot, but for reasons I don't want to...

Homework Statement So I solved this problem ∑ (-1)^n (x+5)^n by finding the sum of the series to be 1/(x+6), which was correct. I am stuck on the second part of the problem asking for interval notation. It says: Determine, in interval notation, the values of x for which the series converges...