What is Limits: Definition and 1000 Discussions

I am reading John B. Conway's book: A First Course in Analysis and am focused on Chapter 2: Differentiation ... and in particular I am focused on Section 2.1: Limits ... I need help with an aspect of the proof of Proposition 2.1.2 ...Proposition 2.1.2 and its proof read as follows: In the...

Quoting from Modern Cosmology by Andrew Liddle on pages 130 and 131: "Let me stress right away that the luminosity distance is not the actual distance to the object, because in the real Universe the inverse square law does not hold. It is broken because the geometry of the Universe need not be...

ok I chose c being false, since a limit does not exist if f(x) is different coming from $\pm$

I've read in several places that some cosmological theories posit the existence of an "infinite number of universes" with laws of physics different from our own. I'm sure there's a lot of shortcutting in the reporting and "infinite" can't really mean infinite, can it? Wouldn't an infinite number...

Hello, I am having issues finding the dominant terms in the following expression: lim [(x^7)-9(e^x)] / [sqrt(10x-1)+8*ln(x)] x->infinity Prompt: Find the limit and the dominant term in the numerator and denominator.

ok I posted a image to avoid any typos but was wondering why the question has dx and options are in dt I picked C from observation but again that was assuming f was a horizontal line of which it could be something else that way the limits stay the same but the area is cut in halfopinions...

Hello everyone! I have been looking for a general equation for any regular polygon and I have arrived at this equation: $$\frac{nx^{2}}{4}tan(90-\frac{180}{n})$$ Where x is the side length and n the number of sides. So I thought to myself "if the number of sides is increased as to almost look...

If n is ∞, then ln (n) = ln (∞) = ∞ Then, 1/∞ = 0 Any number raised to "0" = 1, so the answer should be 1. However the book says the answer is e2. Could you provide me some help?

I don't understand my textbook, so I simply don't understand how to solve this math problem. I really appreciate some help!

Since $$\lim_{x \rightarrow 0} \frac {R_{n,0,f}(x)} {x^n}=0,$$ ##P_{n,0,g}(x)## contains only terms of degree ##\geq 1## and ##R_{n,0,g}## approaches ##0## as quickly as ##x^n##, I can most likely prove this using ##\epsilon - \delta## arguments, but that seems overly complicated. I also can't...

In Physics/Electrostatics textbook, I am in a situation where we have to find the electric field at a point inside the volume charge distribution. In Cartesian coordinates, we can't do it the usual way because of the integrand singularity. So we use the three dimensional improper integral...

238 Solve $$\displaystyle\lim_{h\to 0} \dfrac{\ln{(4+h)}-\ln{h}}{h}$$ $$(A)\,0\quad (B)\, \dfrac{1}{4}\quad (C)\, 1\quad (D)\, e\quad (E)\, DNE$$ The Limit diverges so the Limit Does Not Exist (E)ok the only way I saw that it diverges is by plotting not sure what the rule is that observation...

In five years also experiment KATRIN will give either the upper bound of electron neutrino mass (0,2 eV) or even the mass of the electron neutrino. https://www.katrin.kit.edu/ My question is, what we can expect from the astronomical and non-astronomical measurements to improve these data? I...

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I am reading Charles G. Denlinger's book: "Elements of Real Analysis". I am focused on Chapter 2: Sequences ... ... I need help with the proof of Theorem 2.9.6 (a)Theorem 2.9.6 reads as follows: In the above proof of part (a) we read the following: " ... \forall \ m, n \in \mathbb{N}, \...

Sorry for the silly question! If we start of with the relationship $$\int_{x_{1}}^{x_{2}} F dx = KE_{2} - KE_{1}$$ and then state that at position x1 the velocity (and hence also kinetic energy) of the particle is 0, and at x2 its velocity is v, is it sloppy or valid to write the integral...

I am reading the book: Complex Analysis: A First Course with Applications (Third Edition) by Dennis G. Zill and Patrick D. Shanahan ... I need some help with an aspect of the proof of Theorem 3.1.1 (also named Theorem A1 and proved in Appendix 1) ... The statement of Theorem 3.1.1 (A1) reads...

I am posting some AP calculus practice questions on MeWe so thot I would pass them thru here first The solution is mine... any typos or suggestions... $\textbf{Find the Limit of}$ $\displaystyle\lim_{x\to \pi} \dfrac{\cos{x}+\sin{x}+1}{x^2-\pi^2}$ (A) $-\dfrac{1}{2\pi}$ (B) $\dfrac{1}{\pi}$...

This question consists of two parts: preliminary and the main question. Reading only the main question may be enough to get my point, but if you want details please have a look at the preliminary. PRELIMINARY: Let potential due to a small volume ##\delta## at a point ##(1,2,3)## inside it be...

I want to show that the limit of the following exists or does not exist: When going along the path x=0 the limit will tend to 0 thus if the limit exists it will be approaching the value 0 when going along the path y=0, we get an equation with divisibility by zero. Since this is not possible...

I recently found the centre of mass of a semicircle using polar coordinates, by first finding the centre of mass of a sector, and then summing all the sectors from 0 to pi to get the centre of mass of the semicircle. However, being a beginner at integrals, I struggled for a long time getting the...

So I can push this integral all the way to the end and see I get a negative volume. I solve for the intercepts of the cone and sphere at r^2 = 1/2. Seeing this cone is inside the sphere and the sphere is around it, I figure I should integrate from sqrt(1/2) to 1 since we're dealing with a unit...

I tried substituting x=cos2theta but it was of no use.I thought many ways but i could not make 0/0 form.So please help.

It is of the form (0/0)^infinity. I know how to solve 1^infinity form

I wrote cos(pi(n^2+n)^(1/2)) as cot(pi(n^2+n)^(1/2))/cosec(pi(n^2+n)^(1/2)) and as we know cot(npi)=infinity and cosec(npi)=infinity , so i applied L'Hospital.After i differentiated i again got the same form but this time cosec/cot which is again infinity/infinity.But if i differentiate it i...

I came across this basic limits question Ltx->0[(ln(1+X)-sin(X)+X2/2]/[Xtan(X)Sin(X)] The part before '/'(the one separated by ][ is numerator and the one after that is denominator The problem is if I substitute standard limits : (Ltx->0tan(X)/x=1 Ltx->0sin(X)/X=1 Ltx->0ln(1+X)/X=1) The...

Problem Statement: Determine whether f is continuous at c. (see image for piecewise function f) EDIT: Sorry if it is a little blurry that is x^3 in the numerator of the rational function and x^2 in the denominator Relevant Equations: Basic understanding of limits My work: Since the...

Hi, I remember some sort of method for evaluating limits from Calc 1 that involved substituting in 1/n for x and simplifying. Does that sound familiar to anyone? Sorry I know that's vague, but all I can really remember about it. I can't find it mentioned anywhere in Stewart nor online :/ Thank...

Let: ##\displaystyle f=\int_{V'} \dfrac{x-x'}{|\mathbf{r}-\mathbf{r'}|^3}\ dV'## where ##V'## is a finite volume in space ##\mathbf{r}=(x,y,z)## are coordinates of all space ##\mathbf{r'}=(x',y',z')## are coordinates of ##V'## ##|\mathbf{r}-\mathbf{r'}|=[(x-x')^2+(y-y')^2+(z-z')^2]^{1/2}##...

Summary: Hi all I would like to understand this concept please help. I understand the montonic convergence theorem this is from a probability theory book and I am confused on understanding it. Please help me understand it. Thank you very much,Jon.

With respect to operations, I understand why an integral is multiplied by -1 when its limits reversed. But integral is geometrically an area so reversing the limits would not be able to change neither how large is the area nor the shape of the area. Would you please explain changing the limits...

U= 1/x dV= sin(x) dU = -1/x^2dx V= -cos(x). lim b--> infiniti (integral from [0,b]) = 1/x(-cos(x)) - integral(1/x^2(cos(x)) dx

I want to compute: $$\oint_{c} F \cdot dr$$ I have done the following: $$\iint_{R} (\nabla \times v) \cdot n \frac{dxdy}{|n \cdot k|} = \iint (9z-1) dxdy$$ I don't know what limits the surface integral will have. Actually, I am not sure what's the surface. May you shed some light...

The potential of a dipole distribution at a point ##P## is: ##\psi=-k \int_{V'} \dfrac{\vec{\nabla'}.\vec{M'}}{r}dV' +k \oint_{S'}\dfrac{\vec{M'}.\hat{n}}{r}dS'## If ##P\in V'##, the integrand is discontinuous (infinite) at the point ##r=0##. So we need to use improper integrals by removing...

I am fascinated with data compression, and for the past 7 years i have been trying to create an algorithm that can compress information almost infinitely let's say for example 1GB of information into 1KB of information, and while impossible that sounds after 7 years working at that problem 16...

Hello, I was told every country needs a constant electricity production source (like coal or nuclear powerplants), and up to some proportion, renewable sources (photovoltaics, hydro, wind turbines, etc). So, my question is: what limits the amount of renewable sources? (the grid, storage...?)...

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...

I've been taught that $$1^\infty$$ is undetermined case. Why is it so? Isn't $$1*1*1...=1$$ whatever times you would multiply it? So if you take a limit, say $$\lim_{n\to\infty} 1^n$$, doesn't it converge to 1? So why would the limit not exist?

Let $0<b<a$ and $(x_{n})_{n\in \mathbb{N}}$ with $x_{0}=1, \ x_{1}=a+b$ $$x_{n+2}=(a+b)\cdot x_{n+1}-ab\cdot x_{n}$$ a) If $0<b<a$ and $L=\lim_{n\rightarrow \infty }\frac{x_{n+1}}{x_{n}}$ then $L= ?$ b) If $0<b<a<1$ and $L=\lim_{n\rightarrow \infty }\sum_{k=0}^{n}x_{k}$ then $L= ?$ I don't know...

Hi all. I have a question about something Nima Arkani-Hamed said in his lecture on space-time about space contraction near light speed. I included a link to the lecture at the point where he refers to contraction of two space ships with a 'cable' between them, they are accelerating towards the...

Homework Statement If ##\vec { F } = x \hat { i } + y \hat { j } + z \hat { k }## then find the value of ##\int \int _ { S } \vec { F } \cdot \hat { n } d s## where S is the sphere ##x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4##. The Attempt at a Solution From gauss divergence theorem we know ##\int...

Homework Statement [/B] The path of a baseball relative to the ground can be modeled by the function ##d(t)=−t^2+8t+1## , where d(t)represents the height of the ball in metres, and t represents time in seconds. What is the speed of the ball when it hits the ground? Homework EquationsThe...

Hi! I have wires that have printed 600V 16 AWG on it. I found this table: http://www.basicsofelectricalengineering.com/2017/07/basics-of-wire-gauge-and-awg-system.html . As I understood then long wires can be used to transmit 3.7 amps and short ones 22 amps? Also does it depend on voltages...

Homework Statement Hi everyone, I'm currently making my way through Spivak's calculus and got stuck in question 41 of chapter 5. It's important to note that at this point, the book has only reached the subject of limits (haven't reached continuous functions, derivatives, integrals, series...

I've understood the formal definition of limits and its various applications. However, I'm trying to dive more into the history of how the concept of limits were conceived (more than what Wikipedia tends to cover), and how to formally understand and visualise infinitesimals. For example, I know...

Hello, I have a very specific problem and didn't find any way to solve it. My signal is very slow changing at 5V +-100mV When I want to display this signal on my RIGOL Oscilloscope, the problem is, that with AC-mode I don't see those slow changes and in DC-mode the offset range is limited to...

Homework Statement Please see attached image for the full scope of the problem, and to see the work drawn out by the text. My question lies with line 3 as it is clear that u-substitution was used on a definite integral, but the limits of integration were not changed. Homework EquationsThe...

This is a random problem I am trying to figure out. The context doesn't matter. I wish to define a function z(x, y) based on the following limits: 1. lim z (x→∞) = 0 2. lim z (x→0) = y 3. lim z (y→∞) = ∞ 4. lim z (y→0) = 0

Hi, I got curious on the limits of variatonal principle. As far as i know all of the theories can be reformulated as problem of finding extremum of some action. Not only that, but it seems to be most convenient method for looking for new theories in a lot of cases. So my question is, what are...