What is Limits: Definition and 1000 Discussions

Foundations of "Formal Limits" In Spivak's 4th Edition, one examples says: "The function f(x) = x2 is a little more interesting. Presumably, we should be able to show that f(x) approaches 9 near 3. This means that we need to be small enough to show how to ensure the inequality...

Homework Statement Find the limit: lim (1-cos2x)/(xsinx) x->0 Homework Equations Identities The Attempt at a Solution I've done this over and over and over again! The answer is supposed to be 0 but I keep getting 2 ): lim (1-cos2x)/(xsinx) x->0 lim...

If we have an exponential fuction, (for example) Limx->∞ e(x2+2x+1)/(x2-3) Would we first determine the limit of the "argument" (not sure if right word) of ex and then replace the "argument" with the limit and then evaluate it? So for the example above, The limit of...

Homework Statement The problem asks to integrate dx\(sqrt(abs(x-1))) from 0 to 2. \int(dx/(sqrt(abs(x-1)))) Homework Equations I had the limit as b approaches 1 of the integral (from 0 to b) plus the limit as c approaches 1 of the integral (from c to 2). The Attempt at a Solution...

I'm having a hard time learning from the textbook, I know I can do this if someone just outlines what my goal is here... and what I can interpret from that goal. The solutions handbook just makes seemingly random algebraic changes to the limit function and then tells me what the answer is...

Homework Statement Find the limit as x approaches zero of (2sin5x)/x Homework Equations The limit as x approaches zero of (sinax/x) = a and there's the scalar multiple rule. The Attempt at a Solution Is the answer then 10?

Firstly, I find the math syntax on this board incredibly difficult to use, so bear with me. Using any symbol makes the text appear on the next line... I don't know if it is my browser, or what, but I tried to make due. Sorry. Homework Statement Construct an "epsilon minus delta" proof for...

1. Alternating power series question on convergence interval. I'm wrestling a bit with an alternating power series, the teacher has the convergence interval to be x = <-2,2] and I don't agree.Homework Equations Without further adue, here is the alternating power series in question...

Homework Statement Invert the limits of integration of the following integrals: 1 ) \int_{0}^{4} dx \int_{0}^{x} f(x,y)dy \int_{0}^{2} dx \int_{0}^{\surd (4 - x^2)} f(x,y)dy \int_{0}^{1} dy \int_{y}^{2-y} f(x,y)dx These are 3 different integrals in 3 separate exercises, they're...

Given a function f(x) = lim n->infintiy [x]^n / (x^n +1) , where [x] is a greatest integer function. What is the limit value of lim x->1+ f(x) ? Is the limit found above the same with lim n->infinity (lim x->1+ [x]^n / (x^n +1) ) ? I am rather confused with the above two cases. I...

I had this on a test today. First everything seemed easy, but then I got stuck. So the body over which the integral is to be taken is defined by: 1 <= x2 + y2 + z2 <= 4 and z >= sqrt(x2 + y2) Right now as I'm typing this I just thought that, why not plug z from the second eq. into the...

Hi guys, I've been doing past paper questions for an exam and I've gotten stuck with the limits of an integral. We have to evaluate \int\int\int _{\Omega} \frac{1}{(1+z)^2} dx dy dz where \Omega = \left\{ (x, y, z) : x^2 + y^2 \leq z^2 \leq 1 - x^2 - y^2, z \geq 0 \right\} using spherical...

Homework Statement True/False If f is continuous at 5 and f(5) = 2 and f(4) = 3, then lim x-> 2 f(4x^2 - 11) = 2 Homework Equations lim x-> 2 f(4x^2 - 11) = 2 The Attempt at a Solution This turns out to be true, despite the fact that the limit evaluated without respect to...

I thought quantum entanglement only occur in very isolated environment and laboratory setup. How come photosynthesis use it? Do you know of a website that illustrates how this work in very clear manner? All those paper about the photosynthesis effect are difficult as they are mainly for...

Homework Statement A surface S is defined by z = 1-x^2-y^2 between 0≤ z ≤1 I need to calculate the flux of the vector field F = (y)i + (z)j through S.Homework Equations Cylindrical polar coordinates, Normal etcThe Attempt at a Solution By changing the variables using cylindrical polar...

Homework Statement [PLAIN]http://img9.imageshack.us/img9/4537/unledow.png Homework Equations The Attempt at a Solution Hi, does anyone know how to find the integral that needs to be evaluated here? I can't understand how to find it from the region edit: Oh and this is from here, not a take...

So I'd like to start out by asking why the interchanging of limits is phrased in terms of the property of uniform convergence? Can all double limits be written in terms of the limit of some sequence of functions and the limit as the input variable for these functions approaches some specific...

LIMx\rightarrowinfinite (bn+an)1/n it is given that 0<a<b in this case why do we take bn or an common to make the inside element 0...and how do u guys take to solve this kind of situation how do u think?

Homework Statement Find lim x -> 0 \frac{sin x}{sin\frac{x}{2}} The Attempt at a Solution Since period of sin 2(x/2) is T/2 compared to period T of sin (x/2) sin 2(x/2) nears twice the value of sin (x/2) for all values of x approaching zero. Therefore lim x -> 0 \frac{sin...

http://imageshack.us/photo/my-images/710/unled1vr.jpg/ I don't know how to get the 3 limits, could someone teach me how to do it? Thanks :)

In limits, how do you tell immediately if the only way to solve the problem is to test it out? What are some cases where rewrtiting the equation won't get results? eg. 0.99, 0.999, 0.9999

Homework Statement lim n->infinity (4^x + 7^x)^(1/x) Homework Equations Not applicable (?) The Attempt at a Solution Tried taking "plugging" infinity for n but I keep getting 1, is this right? Seems too easy to be just 1? Thank you.

Homework Statement Why does the limit as x approaches 0 of x^2 + 5 / 3x go to infinity (with 0 as an essential disc.) but without the +5, the function goes to 0? Homework Equations The Attempt at a Solution I tried approaching evaluating the limit of the function by comparing the...

So the general tactic for straight lines: f(x) = 2x Show by epsilon-delta definition of limit, as lim x->2, f(x) tends to 4. let, ε>0, and choose 0<δ<ε/2 (|x - 2|<δ)→ |f(x) - 4| = |2x - 4| = 2|x - 2| < 2δ < ε No problem, but what about for a parabola? g(x) = ax2 for some a in R. Show as lim x...

Homework Statement If you have a 1d infinite potential well between 0 and a which is then expanded to become 0 -2a with the wavefunction in that instant undisturbed, what is the expectation value of energy at that moment. my thoughts are that as the eigenfunction will be the same then...

compute the limit lim as x,y --> (0,0) of (x+y)*ln(x2+y2) i would use polar coordinates if (x+y) was (x^2+y^2) but that not being the case is messing with me. and than another one is the same parameters, but of (x^2*y)/(x^4+y^2). for this one i attempted to do the partial deriv of both x...

I seem to find a problem with the limit lim(x->0) (x^2sin(x)) ----------- 1-cos^2(x) using the limit as x approaches 0 of x over sine of x equals 1 we can simplify as such (x) * (x) * sin(x) ----- ------ sin(x) sin(x) and this would...

Homework Statement For a sequence a_n: If lim (a_n) =2, use the definition of a limit to show that lim (a_n / n) = 0 all limits are as n goes to infinity The Attempt at a Solution I know that I need to show: Give any \epsilon>0 there is some M so that if n>M then |a_n / n| <...

Homework Statement lim x -> infinity : sqrt(x^2 + 4x(cos x) ) - x find the limit (or lack there of) Homework Equations look above The Attempt at a Solution ok so i used the addition/subtraction law to show that the limit of f(x) = - x as x --> infinity = infinity now for the other half...

Homework Statement This question has been literally troubling me for 2 days. Question 2(b) Suppose for some c \in R, 0<c<1, we have |a_{n+1}-L|<c|a_{n}-L| for \forall n \in N (1) Use the sandwich theorem and the fact that\stackrel{lim}{_{n\rightarrow\infty}} c^{n}=0 to prove that...

Hi there, I was reading a novel recently where a character was using telescopes to watch vehicles moving on a planet at many light hours distant. The 'explanation' for his telescopes awesomeness is that it is designed to see distant stars and so seeing people moving on a planet in the same...

Homework Statement Show that \lim_{x\to2}\frac{x+1}{x+2}=\frac{3}{4}. Homework Equations Let \epsilon>0 . We seek a number \delta>0: if |x-2|<\delta then |\frac{x+1}{x+2}-\frac{3}{4}|<\epsilon. The Attempt at a Solution Now...

Homework Statement For f(x) = |x^2-9|/x-3 and a=3, discuss the limiting behavior of f(x) as x->a+, as x->a- and as x->a The Attempt at a Solution Am i right to say that the limit for x-> 3 is undefined? I am also a little confused with the a+ and the a- for a+ i would say that 3+^2-9/3+-3 =...

Basically, find the limit of the sequence: {[(n+3)/(n+1)]^n}, from n=1 to infinity Book says it's supposed to be e^2, and indeed the graph shows that... I'm not sure what to do with the top of the fraction. Working with the bottom and dividing by n, I obtain, lim as n approaches...

Homework Statement Let S be the part of the plane z=f(x,y)=4x - 8y +5 above the region (x-1)^2 + (y-3)^2 <= 9 oriented with an upward pointing normal. Use Stoke's theorem to evaluate the surface integral for the vector field <2z, x, 1>. Homework Equations Stoke's Theorem is surface...

How can i show that both limits exist and are equal to 0? I attached limits as bmp file "i" refers to "i times" not complex number so you can ignore. This formula is calculated after analysis of algortihms by using summations.

OK, our Calc professor gave us a paper with some limits to calculate, but I'm not quite sure about them...Here are some examples: a)lim (5x^5+3y^5)/(x^2y^2+1) x->0 y->0 Since the obvious replacement is too suspicious, I thought about looking if it exists by using the y=mx line...

first I'm a new user and i want to say thank u for such a forum my question is for two trayectories 1st y = x 2nd x = 0 meant to calculate the limit of (3x^2*y)/(x^2 + y^2) as (x,y) approaches (0,0) first trayectory: lim (3x^2*y)/(x^2 + y^2) = 3x^3/2x^2 = (3/2)x second trayectory: lim...

Homework Statement Find the limit of ((x^3 + (4x^2)y)/(x^2+2y^2)) as (x,y) -> (0,0) Homework Equations The Attempt at a Solution I am guessing the limit is equal to 0, and I know I have to use 0 < sqrt(x^2 + y^2) < delta where |f(x,y) - L| < epsilon I just have no idea what to do next I...

Homework Statement Find the limit as x approaches 0 of xsin(1/(x^2)) Homework Equations The Attempt at a Solution I think this goes to 0, because the sine component just oscillates between 1 and -1, and gets multiplied by 0, for all x. I don't know how to show this using limit...

Homework Statement Evaluate the following limit or give a reason explaining why the limit does not exist. \lim_{(x,y) \to (0,0)}\frac{x-y}{x+y} Homework Equations x = r*\cos\theta y = r*\sin\theta The Attempt at a Solution \lim_{r \to...

Ive come across a few derivations whereby a few changes that don't see so obvious to me occur. For instance, this one: Integral, from 0 to infinity, of x.sin(ax), whereby it becomes x.exp(iax) / 2i, from minus infinity to plus. How can the limits be changed like that, and what about the...

a) Suppose that the limit as n goes to infinity sn=0. If (tn) is a bounded sequence, prove that lim(sntn)=0. So I need to show that abs(sntn)<epsilon, and I know that abs(sn)<epsilon. I mean, I know abs(sntn)=abs(sn)abs(tn that didn't help. I don't know how to go about this. I've tried the...

lim (sin⁡(n)/n)=0. The instruction say I can only use the definition of limit and no additional theorems. So the first thing I should do is figure out if l sin(n)/n l < epsilon, find out what n is greater than. I can pull the 1/n out of the absolute value, but I don't know how to get the sine...

Multivariable Limits! Lim (x^2+y^2)/(1+y^2) (x,y)--> (0,0) evaluate the limit or determine that it does not exist. Im pretty sure that the limit does not exist because if i take it from the y and x axises the values don't match up but not really sure if that is the right way to do it. Any...

Hi! I am an amateur to the world of calculus... I have a doubt with the limits in case of functions which are vectors... Actually, I require it's application in physics... Suppose we have a vector r (all vectors in bold face), which represents the general position vector of a point on any...

What is wrong?

uniqueness of limits: please check which answer i should use :) Prove that in a metric space (X, d) limits are unique. [xn] -> x and xn ->y then x = y By contradiction: Assume x =y. let |x - y|/3 (Can I just make a random assumption like this?) |x - y| = |f(x) - x|+|f(x) - y| defn of a...

http://arxiv.org/abs/1102.2784 New Limits on Planck Scale Lorentz Violation from Gamma-ray Burst Polarization Floyd W. Stecker 3 pages, submitted to Phys. Rev. Letters (Submitted on 14 Feb 2011) "Constraints on possible Lorentz invariance violation to first order in E/M_{Planck} for photons...

Need help in finding Limits of Integration! :) (Calc 3) Homework Statement Evaluate Integral: f * n dS, where "f" and "n" are vectors and "*" is DOT PRODUCT. Where, where (a) f = (x2, ey, 1), S: x + y + z = 1, x ≥ 0, y ≥ 0, z ≥ Homework Equations ummm none The...