What is Limits: Definition and 1000 Discussions

if $\lim_{{n}\to{\infty}} {y}_{m+1}={x}^{*}$, Can we say that $\lim_{{n}\to{\infty}} {y}_{n-1}={x}^{*}$...Please pay attention, I say m and n...

In the example in the picture, we can see that they chose the limits of integration to be from 0 to R_0. Why didn't they choose x (that is, from 0 to x)? Isn't that what we normally integrate over when we find potential energy and electric fields? Thank you

lim xm-1/xn-1 m,n elements of N x→1 the answer is m/n but i have no idea how to start or solve this!

find the one sided limit at the point x=0 for functions f(x)={ sinx/x, x greater than 0 ; x+1, x less or equal than 0

Homework Statement Evaluate ##\lim_{x\to 0} \frac{2^x-1-x\log_e2}{x^2}## without using L'Hospital's rule or expansion of the series. Answer is given to be = ##\frac{(\log_e (2))^2}{2}## Homework Equations Squeeze play theorem/ Sandwich theorem, some algebraic manipulations and standard...

So if we become a Kardashev type II civilization, able to harvest all the energy and matter in the solar system what could we see through the massive telescopes that would be possible to construct? (say with a lens the size of Saturn). Could you get surface detail on extrasolar planets, for...

This may be a very basic question for this forum. I have just started to Learn Calculus. Please. help me with my question - Suppose I need to find the Limit of 1/x where x tends to 0 from positive side. I know from the graph of 1/x that answer is +Infinity. But if I apply Squeeze...

Homework Statement Find tangent line of y=xe^{\frac{1}{x}} at point x=\alpha and it's limit position when \alpha \rightarrow +\infty. Homework Equations Tangent of y=f(x) at point M(x_0,f(x_0)): y-y_0=f^{'}(x_0)(x-x_0) The Attempt at a Solution Applying the above equation for tangent of...

Homework Statement [/b] Determine if the limit exists as a number, ∞, -∞ or DNE lim x->4- -(2)/(sqrt(4-x)) The Attempt at a Solution lim x->4-... I honestly don't know how to solve. Because I don't know what to do with the sqrt function. If someone could lead me in the right direction here...

$$\lim_{x\to\infty} \frac {frac(x)} {x} $$ frac(x) is x minus floor function of x. So if x = 2.5, floor function = 2 and frac(x) = 0.5 Hence frac(x) will always be a number between -1 and 1 but never -1 and 1. By squeeze theorem, -1 < frac(x) < 1 -1/x < frac(x)/x < 1/x 0 < frac(x)/x < 0 Does...

## \int_{0}^{∞}\int_{0}^{∞} \frac{x^2+y^2}{1+(x^2-y^2)^2} e^{-2xy} dxdy ## ##u= x^2-y^2## ##v=2xy##I tried to find the jacobian and the area elements, I found it to be ## dA = \frac{1}{v} du dv ## I'm having problem finding the limits of u & v and getting rid of ##x^{2}+y^{2}##.

I am confused about the algebraic process of finding a limit. Let us take ##\frac{x^2 -1}{x - 1}##. In trying to find ##\lim_{x\rightarrow 1}\frac{x^2 -1}{x - 1}##we do the following: ##\displaystyle\lim_{x\rightarrow 1}\frac{(x+1)(x-1)}{x - 1}## ##\displaystyle\lim_{x\rightarrow 1}x+1##...

Homework Statement ##f(x)## is a continuous and differentiable function. ##f(x)## takes values of the form ##^+_-\sqrt{I}## whenever x=a or b, (where ##I## denotes whole numbers) ; otherwise ##f(x)## takes real values. Also, ##|f(a)|\le |f(b)|## and ##f(c)=-1.5##. Graph of ##y=f(x)f'(x)##: The...

The speed of light is the universal speed limit and absolute zero is the universal temperature limit. Are there any other universal limits like this in nature?

Hi guys...i'm a little naive...i encountered the limit of this function: Sin(x^-1) x as the x goes to infinity...in order to study it i know that i have to find the Taylor series about the function Sin(t) centered in 0 having defined t=(x^-1)...something called asymptotical expansion of...

I want to evaluate \displaystyle\lim_{(x,y)\to(-1,0)}\frac{y^4(x+1)}{|x+1|^3+2|y|^3} With some help, I was able to prove that the limit is 0, using Hölder's inequality. Like this: \left(|x+1|^3\right)^{1/5}\left(\frac{1}{2}|y|^3\right)^{4/5}\leq\frac{1}{5}|x+1|^3+\frac{4}{5}\frac{1}{2}|y|^3...

Hello , i was just wondering if anyone could clarify one thing in this proof (its from Konrad Knopp book on infinite series) : If (x0,x1,...) is a null sequence, then the arithmetic means xn'= x0+x1+x2+...+x/n+1 (n=1,2,3,...) also forms a null sequence. Proof: If ε >0 is given, then m can be...

Homework Statement Find f ' (x) if f(x) = 4x + 4 / x2 + 4 Homework Equations I used the mnemonic "lo dhi - hidlo / (lo)^2 The Attempt at a Solution I got -4x^2 +16-8x / (x^2+4)^2 but it's telling me I'm wrong? Why? I computed it again but I still got the same answer.

Homework Statement Given that lim f(x) = -4 and lim g(x) = 6 (All limits x --> +infinity) Find the limit lim [f(x) + 2g(x)]Homework Equations The Attempt at a Solution So I substituted the values of f(x) and g(x) in the equation...

Homework Statement Use the ε-δ definition of limits to prove that limx→2 x2 = 4. The Attempt at a Solution |x2 - 4| < ε 0 < |x - 2| < δ |x - 2| |x + 2| < ε And that's where I get stuck, can I divide both sides by |x + 2| to yield |x - 2| < ε/|x + 2| = δ In which case, where do I go from...

< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown > This is from the question list at the UC Davis Website epsilon delta exercise list. In the exercise list we have: Prove that Which concludes with: Thus, if , it follows that...

Both string theorists and loop quantum gravity theories have proposed that space-time may be something other than the perfectly smooth, perfectly local space of classical general relativity, which can potentially lead to path dependent phase alteration of light from a common source due to the...

I'm taking an online coursera course and the guy is explaining limits. He doesn't really explain why he does this numerator thing.

I've been searching around trying to understand them. About to take calculus and I want to be prepared. Could someone explain what they are and give a few typical limit problems and solve them Thank you

Can someone rephrase the title question into something more meaningful in terms of Calculus/Analysis?

There is only one way to reduce the equations of special relativity (aka Lorentz Transformations) to the equations of Newtonian mechanics (aka Galilean Transformations). In light of the above, why are there multiple ways to reduce quantum-mechanical equations of motion into classical equations...

Homework Statement Hello all, I am having hard time with limits. 1. limx->1- x/ln(x) 2. limx->1+ x/ln(x) Homework EquationsThe Attempt at a Solution 1. limx->1- x/ln(x) = 1-/ln(1-) ln(1-) = 0- I seriously don't understand why ln(1-) = 0- 2. limx->1+ x/ln(x) = 1+/ln(1+) ln(1+) = 0+ I...

Homework Statement 1. f(x) = (1+x)1/x lim x->0+ (1+x)1/x 2. lim x->0+ 10+ln(x) Homework EquationsThe Attempt at a Solution 1. lim x->0+ (1+x)1/x (1+0+)1/0+ I really don't understand how the final answer is e... thanks for helping. = e12. lim x->0+ 10+ln(x) ln(0+) = -infinite 10 - infinite...

http://tutorial.math.lamar.edu/Classes/CalcI/LimitsAtInfinityI.aspx According to the author, if ##c## is a real number and ##r## is a positive rational number then: $$\lim_{x →\infty} \frac{c}{x^r} = 0$$ If ##x^r## is defined for ##x < 0## then: $$\lim_{x →- \infty} \frac{c}{x^r} = 0$$ I...

Homework Statement hello in the college we have Fourier series and i have a problem with the integral limits i add a pdf ( 2 pages only) my question is: how did he get the integral limits from the question the limits are from ##-\pi## to ##-\frac{\pi}{2}## for f(x)=-2 as shown in the first...

Homework Statement Calculate \lim_{(x,y)\to(0,0)}\frac{x^4-4y^2}{x^2+2y^2} along the the line y=2x Homework Equations N/A The Attempt at a Solution Not too sure what they mean by calculating the limit along the line y=2x. The answer is \frac{-3}{5}. But I have gotten so far...

Homework Statement Consider the following geodesic of a massless particle where ##\alpha## is a constant: \dot r = \frac{\alpha}{a(t)^2} c^2 \dot t^2 = \frac{\alpha^2}{a^2(t)} Homework EquationsThe Attempt at a Solution Part (a) c \frac{dt}{d\lambda} = \frac{\alpha}{a} a dt =...

Homework Statement I am trying to work the moment of inertia for a) rotating rod, axis through the centre of the rod http://hyperphysics.phy-astr.gsu.edu/hbase/mi2.html#irod3 b) Solid cylinder http://hyperphysics.phy-astr.gsu.edu/hbase/icyl.html#icyl2 [/B] Homework Equations I = R^2 dM The...

Homework Statement Hi Guys, This is the first exampe from Engel's problem solving book. After a long period of no math I am self studying. I do not know where my knowledge deficits lie, and was recommended this site for help. "E1. Starting with a point S (a, b) of the plane with 0 < b < a...

I am studying general relativity from Hobson and came across the term 'lifetime' of a closed (k>0) universe, ##t_{lifetime}##. I suppose at late times the curvature dominates and universe starts contracting? Are they simply referring to ##\int_0^{\infty} dt##? If so, would the bottom expression...

Homework Statement The question asks me to convert the following integral to spherical coordinates and to solve it Homework EquationsThe Attempt at a Solution just the notations θ = theta and ∅= phi dx dy dz = r2 sinθ dr dθ d∅ r2 sinθ being the jacobian and eventually solving gets me ∫ ∫ ∫...

Homework Statement Evaluate the triple integral: ∫ x dxdydz A where A = {(x; y; z) : x, y, z > 0, x + y + z ≤ 1} . Homework Equations None that I know of. The Attempt at a Solution The problem I have is determining the limits for x, y and z. I don't really understand the following...

I claim that if a function ##f:\mathbb{R}\rightarrow\mathbb{R}## is continuous at a point ##a##, then there exists a ##\delta>0## and ##|h|<\frac{\delta}{2}## such that ##f## is also continuous in the ##h##-neighbourhood of ##a##. Please advice if my proof as follows is correct. Continuity at...

Homework Statement F(x)= x^2*{Cos(Pi/x)} when x!=0 (Not equal to)[/B] 0 when x=0 Is the function differentiable at x=0 ?? P.S.- Cos(pi/x) is under mod (Absolute value) 2. Homework Equations - Basic limit formulas.The Attempt at a Solution I...

Hi guys, just having some confusions on the Delta-Epsilon proofs for multivariable limit functions. here is my question: Apply Delta-Epsilon proof for the Lim (x,y) --> (0,0) of (y^3 + 5x^2y)/(y^2 + 3y^2) to show the limit exists. The part that has me confused is the y to the power of 3, where...

Homework Statement Derive the momentum for a charged particle going through matter. Homework Equations None. The Attempt at a Solution I understand the derivation but there's one step I am not clear about, and I'm probably being really stupid but this: if the -infinity term is squared then...

Ok so what I want to know is, is this valid? If so what does it mean?

A video on time reversal inspired me to attempt a version of Conway's "life" that would share QM's T-symmetry. If you have never hear of Conway's life, it is described here: http://en.wikipedia.org/wiki/Conway's_Game_of_Life My thought was that instead of the two colors (black and white) in...

Homework Statement Let f_1,f_2\colon\mathbb{R}^m\to\mathbb{R} and a cluster point P_0\in D\subset\mathbb{R}^m (domain) Prove that \lim_{P\to P_0} f_1(P)\cdot f_2(P) = \lim_{P\to P_0} f_1(P)\cdot\lim_{P\to P_0} f_2(P) Homework EquationsThe Attempt at a Solution Let \begin{cases} \lim_{P\to...

Homework Statement Prove that : $$\lim_{x\to 0}\frac{tan^{-1}x}{x}<1$$ And $$\lim_{x\to 0}\frac{sin^{-1}x}{x}>1$$ Homework Equations None The Attempt at a Solution I have to prove that arctanx has to be lesser than x. It's derivative is 1 at x=0 and keeps decreasing as x increases. So it's...

Hey! :o I have to calculate the following limits, if they exists. $$\lim_{(x, y) \rightarrow (0, 0)} (x^2+y^2+3)$$ $$\lim_{(x, y) \rightarrow (0, 0)} \frac{xy}{x^2+y^2+2}$$ $$\lim_{(x, y) \rightarrow (0, 0)} \frac{e^xy}{x+1}$$ $$\lim_{(x, y) \rightarrow (0, 0)} \frac{\cos...

This is actually a physics problem, but since my question is really about the math involved, I decided to post it in the calculus subforum. I'm supposed to get from the term: $$\lim_{\Delta t → 0} |\vec{v}_r (t + \Delta t)| \frac{\sin \Delta \theta}{\Delta t}$$ To: $$v_r (t) \frac{d\theta}{dt}$$...

Homework Statement (hebrew) : f(x) a continuous function. proof the following Homework Equations I guess rules of limits and integrals The Attempt at a Solution I've tried several approaches: taking ln() of both sides and using L'Hospitale Rule. Thought about using integral reduction...

Hey! :o In my notes there is the following example about the energy method. $$u_{tt}(x, t)-u_{xxtt}(x, t)-u_{xx}(x, t)=0, 0<x<1, t>0 \\ u(x, 0)=0 \\ u_t(x, 0)=0 \\ u_x(0, t)=0 \\ u_x(1, t)=0$$ $$\int_0^1(u_tu_{tt}-u_tu_{xxtt}-u_tu_{xx})dx=0 \tag 1$$ $$\int_0^1...

What limits the speed of information through a copper wire? What is the speed of signal in optic fibres? Is it faster and why?