Limit Definition and 999 Threads

Homework Statement can you cancel the x and the |x|[/B] lim x→0 ( x(1-(cos(x))/|x| ) 2. Homework Equations The Attempt at a Solution At first i thought the limit would just be undefined as x approaches 0 but the answer to the problem is actually 0, so can you just cancel the x with the...

Homework Statement Find the limes of the equation, so lim n -> ∞ Homework Equations [/B] The Attempt at a Solution I tried to solve this by using the third binomial formula and formed this to I wanted to show that it's <= 1/n, but then I checked wolfram alpha and it seems like it actually...

Homework Statement [/B]Homework Equations delta(x) = [b-a]/n xi=a+delta(x)i The Attempt at a Solution So, it is said that i have to use riemann sums to solve this one. what i did is i took the 1/12k out thus getting 1/12k[1/[1+1/12k] + 1/[1+2/12k] + 1/{1+19k/12k]] I found that xi =...

Homework Statement $$\lim_{x \to -∞}{\sqrt{x^2 + bx + c} - x}.$$Homework EquationsThe Attempt at a Solution So in problem 1, once I got to a point where I am to divide by the highest power in the denominator(x) I get something like: $$\lim_{x \to -∞}\frac{bx+c}{\sqrt{x^2+bx+c}+x}$$ Now what I...

Q's Let f,g ℝ→ℝ. Suppose that g is bounded. This means that its image is bounded or in other words there exists a positive real number B s.t. |g(x)| ≤ B ∀ x. Prove that if lim x→c f(x) = 0, then lim x→c f(x)g(x) = 0. Work. See the picture. I am really confused I can't seem to understand the idea...

Hello! I have a question that has been bothering me since I first started learning about Special Relativity: Given only the Minskowskian metric and/OR the spacetime interval, how can one reach the conclusion that the speed of light is invariant for every observer and how can one conclude that it...

This question comes from the equation E = vB (moving conductor in a magnetic field -- E = electric intensity, v= speed of the conductor's movement, and B = magnetic field strength). Say B is constant, so the only thing we have to rely on to vary the electric intensity in the conductor is its...

Dear PF Forum, What is the limit of acceleration? I've been reading old threads, and I found this. G = 6.673 x 10-11 N m2/kg2 Solar mass = 1.989 * 1030kg And I tried to plug in some numbers... In a distance 30 km from a 10 solar mass object the acceleration is... ##a =...

What does it mean for a ##f(x,y)## to be differentiable at ##(a,b)##? Do I have to somehow show ##f(x,y)-f(a,b)-\nabla f(a,b)\cdot \left( x-a,y-b \right) =0 ##? To show the function is not though, it's enough to show, using the limit definition, that the partial derivative approaching in one...

Hello! (Wave)Suppose that $B_{\epsilon}=\{ |x- \xi|< \epsilon\}$ and $E(|x- \xi|)=\left\{\begin{matrix} \frac{1}{(2-n)w_n}|x-\xi|^{2-n} &, n \geq 3 \\ \\ \frac{1}{2 \pi} \ln{|x-\xi|} &, n=2 \end{matrix}\right.$ So when $ |x- \xi|=\epsilon $ then $$E(|x- \xi|)=\left\{\begin{matrix}...

I am reading through Bailin and Love's argument (see P.151-152 of 'Introduction to Gauge Field Theory') that as ##Q^2 \rightarrow \infty##, we probe the product of the two electromagnetic currents appearing in the hadronic tensor for DIS on the lightcone. I will write out the argument here and...

In making cosmological measurements, we are limited to the region within the particle horizon, the 'observable universe'. However, it is reasonable to assume that even if the universe is finite, it is much larger than that volume. If, for example, we measure the curvature ##\Omega_K##, the value...

$$x_n = (-1)^n {2n\over n+1} \sin n $$ it is given that , $$|x_n| = |(-1)^n| {2n\over n+1} |\sin n| < {2n\over n+1} < 2$$ thus bounded, but what i did not get is how did we find ##\lim_{n \to \infty} |(-1)^n| {2n\over n+1} |\sin n| = 2##. I checked with wolfram alpha and it says ##\lim_{n \to...

The limit below represents the slope of a curve y=​f(x) at the point​ (a,f(a)). Determine a​ f After finding the f(x) and a, I did this:8(3^2+3h(3)+3h(3)+h^2)-72 dividing by h getting h(8h^2+144) dividing by h; canceling the h's and the plugging in the limit h --> 0 getting 144. But I am...

My Work: How do evaluate this limit because i will get 2.6667 and divide by -144 it will get me 55.38446... I know that the answer is WRONG but I can't figure it out. Then after that i have to plug in into tangent line y-f(a) = Mtan(x-a) what i am doing wrong. The Problem:

Hello good evening to all, I was studying here and got stuck with this. I solved the integral and got [x+sin(x) -1] and that´s the farthest that I got. I would appreciate the help.

In my rough understanding Molecular Dynamics using Classical Newtonian mechanics is a 6N dimensional non linear system. 6N dimension because you have 3 position vectors and 3 momentum vectors for each N particles. Nonlinearity because of the terms in force fields. In principle this system can...

[FONT=Arial Black]The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual. μx̄ = μ = 12,749 σ = 1.2 n = 35 For the given sample n = 35, the probability of a sample mean being less than...

Homework Statement Find the limit of the function ( attached) Homework EquationsThe Attempt at a Solution Is the limit infinity. Found the integral as (-1/(2t))*e^-2t from 0 to 0. Isn't the integral of a function that is 0 to 0, 0. The lim of 1/x approaching zero infinity.

I am trying to use two limit switches(this one) and two DPDT relays to control the direction of the motor. When the power is applied the motor should rotate one direction (direction for this question isn't important). Also, at this point (initialization) neither switch will be energized. The...

How to solve $$\lim_{x\rightarrow\frac{\pi}{2}}\frac{\cos{x}}{x-\frac{\pi}{2}}$$? At first I tried to convert cos x to $$\frac{\tan{x}}{\sin{x}}$$ but then realized that $$\lim_{x\rightarrow c}\frac{\tan{x}}{x}$$ only applies if c = 0. So, how?

Homework Statement Algebraically solve the following limit, show all work: $$\lim_{x\to0^-} \frac{e^x\cos(x)}{x}$$ Homework Equations I don't know exactly how to go about doing this, but I think I can use the Squeeze Theorem somewhere in here: ##g(x) \leq f(x) \leq h(x)## If ##\lim_{x\to a}...

Hi Everybody, I've seen that one of the reasons that elements past 137 can't be created is because any element past 137 would require electrons in inner orbitals to go faster than the speed of light, and past 137 they would have to. I have also heard that electrons don't literally orbit the...

$\tiny{242.ws8.d}$ $$\displaystyle L_d=\lim_{x \to \infty} \left[\frac{\arctan{(n)}}{\pi +\arctan{(n)}}\right] =\frac{1}{3}$$ $\text{L' didn't work}$ ☕

$\displaystyle L_b=\lim_{x \to \infty} \left\{\frac{n^2}{2^n}\right\} \implies\frac{\infty}{\infty} \\ \text{take natural log of both sides} \\ \ln\left(L_b{}\right)=\lim_{x \to \infty} \left\{\frac{2\ln\left({n}\right)}{n\ln\left({2}\right)}\right\} \\ \text{not sure?? } $

Homework Statement hello, i have to find the limit of the next array (xn)=(cos (π/n+1) + cos (π/n+2) + ...+ cos ( π/2n))/n when n goes to infinity. Homework Equations I was told to apply stolz cesaro and that is where i ended up : the limit is : limit of cos ( π/2n+1) + cos (π/2n+2) -cos...

Homework Statement http://prntscr.com/cpbr3f Homework EquationsThe Attempt at a Solution If I were to simply plug in 25 into the limit, i would get ((25)^(1/3) - 5)/25 Apparently the answer is 2/5. How the heck can you come to this conclusion?

Homework Statement a) Derive the Rayleigh-Jeans distribution by taking the low-frequency limit of Planck's distribution. b) Derive the Wien distribution by taking the high-frequency limit of Planck's Distribution. Homework Equations ## u(f) = \frac {8 \pi f^2} {c^3} \frac {hf} {e^{\frac...

1. Homework Statement Show that d=(9M/(4*pi*p))^1/3 is an approximation for the roche limit. Note that x/d <<1 with M = mass of the primary p = density of the secondary x= distance of a test particle from the center of the secondary (in part a) of the task one should give the motion equation...

Homework Statement Function is ##lim_{(x,y,z) \rightarrow (0,\sqrt\pi,1)} \ e^{xz} \cos y^2 - x## Homework EquationsThe Attempt at a Solution As ##x \rightarrow 0## along ##y= \sqrt \pi, z=1##, ##f(x,y,z)= -1## As ##y \rightarrow 0## along ##x=0, z=1##, ##f(x,y,z) = -1## As ##z \rightarrow...

Homework Statement This is the function: ##\lim_{(x,y) \rightarrow (0,0)} \frac{(x+y)^2}{x^2+y^2}## Homework EquationsThe Attempt at a Solution So for ##x \rightarrow 0## along ##y=0##, ##f(x,y)=1## For ##y \rightarrow 0## along ##x=0##, ##f(x,y)=1## also. But the answer says there is no...

Homework Statement Limx-->positive infty arctan(1+x)/(1-x) Homework EquationsThe Attempt at a Solution I just need to know if my answer is right. Knowing that when the leading coefficients of the x when its the same, then the answer is just the ratio. So it would be -1. Then in my calculator...

Homework Statement Find the limit $$\lim_{x\to-\infty} \frac{\sqrt{9x^6 - x}}{x^3 + 9}$$ Homework Equations N/A The Attempt at a Solution To solve this, I start off by dividing everything by ##x^3##: Numerator becomes ##\frac{\sqrt{9x^6 - x}}{x^3} = \sqrt{\frac{9x^6 - x}{x^6}} = \sqrt{9 -...

Homework Statement Limx--> ∞ Ln(x^2-1) -Ln(2x^2+3) Homework EquationsThe Attempt at a Solution Ln(x^2-1)/(2x^2+3) Then I divided the top and bottom by x^2 so in the end I got (1/2). Is this right?

Homework Statement lim as x tends to -∞ (x)^3/5 - (x)^1/5 Homework EquationsThe Attempt at a Solution The first thing I did was convert it into a radical so it becomes fifthroot√x^3 - fifthroot√x. Then I rationalized to get ( x^3-x)/(fifthrt√x^3+fifthroot√x) . I then divided the top by x^3...

I am trying to find the limit of ## \frac {z^2 + i}{z^4 - 1} ## as ## z ## approaches ##i##. I've broken the solution down to: ##\frac {(z + \sqrt{i})(z - \sqrt{i})}{(z+1)(z-1)(z+i)(z-i)} ## but this does not seem to get me anywhere. The solution says ## -0.5 ## but I don't quite understand how...

Homework Statement Is it true that e find that the function is undefined and we can't simplify them, then the limit of multivariable function is surely doesn't exist http://imgur.com/a/cihXu Homework EquationsThe Attempt at a Solution Is it possible that we already try many different of y...

Does a limit exist on a graph at (-1,0) if the point is solid, and has a right sided limit, but there is nothing left of the point? I understand that if the left sided limit and the right sided limit are different then it doesn't exist, but on my graph it shows a line coming from the right...

Homework Statement I'm looking at an electric field plot around four (4) + and - point charges in free space. There are several points where the electric fields come together and make right-angled turns (in the limit). Is there a name for these points? Especially is there a traditional name for...

Hello I am struggling with proving theorem 1, pages 98-99, in Spivak's Calculus book: "A function f cannot approach two different limits near a." I understand the fact that this theorem is correct. I can easily convince myself by drawing a function in a coordinate system and trying to find two...

Homework Statement limit h goes to 0 sqrt(73-2(x+h))-sqrt(73-2x)/h Homework EquationsThe Attempt at a Solution I am not too sure how to cancel out the "h" in the denominator. just need some hints for me to start

Homework Statement Given r(t)=\left< \frac { sint }{ t } ,\frac { { e }^{ 2t }-1 }{ t } ,{ t }^{ 2 }ln(t) \right> Re-define r(t) to make it right continuous at t=0 Homework EquationsThe Attempt at a Solution This is probably the simplest problem ever, but I don't even know what it's asking...

Homework Statement How to integrate this? ##\int_{0}^{A} x e^{-a x^2}~ I_0(x) dx## where ##I_0## is modified Bessel function of first kind? I'm trying per partes and looking trough tables of integrals for 2 days now, and I would really really appreciate some help. This is a part of a...

Homework Statement Proof that: ##\lim_{x \to 1} \frac{1}{1+x} = \frac{1}{2}## using the epsilon-delta definition of a limit. (Problem below) Homework Equations ##\lim_{x \to 1} \frac{1}{1+x} = \frac{1}{2} \iff \forall ε>0, \existsδ>0, \forall x ∈ \mathbb{R}\backslash\{-1\}: 0 < |x-1| < δ...

1. Problem statement Q. Use limit to find the instantaneous velocity at time t if the postition is p(t) at time t. p(t) = t + (1/t) at x = t 2. Homework Equations (Sorry dashes are in there to keep everything where it should be. I don't know how to make fractions in this and it was...

Hi. How can I prove $$\lim_{n\to\infty} \cos(\alpha/n)^{2n}=1$$ for all ##\alpha\in\mathbb{R}##? The physical background is Malus' law for perfect linear polarizers, I'd like to show that one can losslessly rotate a linearly polarized wave by any angle by stacking an infinite number of...

Homework Statement Given the wave function of a particle \Psi(x,0) = \left(\frac{2b}{\pi}\right)^{1/4}e^{-bx^2} , what is the probability of finding the particle between 0 and \Delta x , where \Delta x can be assumed to be infinitesimal. Homework EquationsThe Attempt at a Solution I proceed...

Hi! First time poster, I'm about to enter first year calc and thought that I could get ahead of the curve by checking out some questions beforehand. This showed up on one of the university calculus exams but I couldn't figure out how to do it. I tried to finding a common denominator but then was...

I am confused about Einstein's thinking. I understand when he formulated his general theory of relativity, he wanted to incorporate 3 foundations for his theory: The relativity principle, the equivalence principle, and Mach's Principle. He believed that inertia and weight were essentially the...

Homework Statement Hey I'm trying to prove the rigorous definition of limit for the following function: Lim (x,y) approaches (1,1) of f(x,y)=(y*(x-1)^(4/3))/((x/1)^2+abs(x)*y^2) Homework Equations abs(x^2)<abs(x^2 +y^2) The Attempt at a Solution I know the rigorous definition of limit. I...