Limit Definition and 999 Threads

Homework Statement For $$\lim _{ x\rightarrow \infty }{ \frac { { x }^{ 2 }+{ e }^{ -{ x }^{ 2 }\sin ^{ 2 }{ x } } }{ \sqrt { { x }^{ 4 }+1 } } } $$, determine whether it exists. If it does, find its value. if it doesn't, explain. Homework Equations Sand witch theorem and arithmetic rule...

Homework Statement Evaluating the following formula: The Attempt at a Solution Since the integral part is unknown, dividing the case into two: converging and diverging If converging: the overall value will always be 0 If diverging: ...?

Homework Statement Hi, I have been trying to find the limit of the following expression in order to determine the Big-o(in particular, the order of decaying to zero) \lim_{x\rightarrow 0} \frac {\cos (x) -1 +\frac {x}{2} }{x^4} Is there another "reasonable" way to solve it? Thank you...

Homework Statement 1. Lim x→0 Sin(x) * sqrt(1 + 1/x^2) Picture: https://i.gyazo.com/2f61c3c09d32447d4190fbdcd3f2f1e5.png 2. Limx→0 Sin(x)/sqrt(x^2 + x^3) Picture: https://i.gyazo.com/b50081d459ed61bcf1d4ae5baecfa7fa.pngHomework EquationsThe Attempt at a Solution What I did with the first was...

I regret to say that I know little of engineering, but, to make a long story short, I'm nagged by two questions about energy conversion efficiency. There is a thread i made titled "giant railguns recycling their own energy in space" in the science fiction & fantasy forum here that explains my...

Homework Statement ##\lim_{\alpha\to\omega}-\frac{\alpha r_0}{\omega(\omega^{2}-\alpha^{2})}\sin(\omega t)+\frac{r_0}{\omega^{2}-\alpha^{2}}\sin(\alpha t)## Homework Equations I feel I will need to use fact ##\frac{d}{d\omega}\sin(\omega t)=t\cos(\omega t)## The Attempt at a Solution [/B]...

Homework Statement Evaluate ##\lim_{a \rightarrow b} \frac{a^b-b^a}{a^a-b^b}## The attempt at a solution I applied L'Hospital's rule and to differentiate it, I took the help of logs.

Homework Statement Calculate: PLIM (probability limit) \frac{1}{T} \sum^T_{t=2} u^2_t Y^2_{t-1} Homework Equations Y_t = \rho Y_{t-1} + u_t, t=1,...T, |\rho| <1 which the autoregressive process of order 1 E(u_t) = 0, Var(u_t) = \sigma^2 for t cov(u_j, u_s) = 0 for j \neq s The Attempt...

Homework Statement lim (x)(sin(1/x)) x->∞ Homework EquationsThe Attempt at a Solution The correct answer is 1, however I do not understand why. I thought that 1/∞ is essentially 0 and sin(0) = 0 so the whole limit would be 0. When I graphed it, the limit did seem to approach 1 though. I...

Homework Statement For f(x,y) = (2x - y^2)/(2x^2 + y), what is the limit as (x,y)->(0,0)? Homework EquationsThe Attempt at a Solution From this image, it seems that the limit would be non-existent since on one side of the sheet, it goes up and up to infinity whereas from the other side, it...

I am designing a custom socket for an application at work and I am concerned about the wall thickness in the area marked by the red box (see attached drawing). The socket will be used to torque a nut to 500Nm. I have a degree in mechanical engineering and I can do stress calcs on straight...

Homework Statement Let ##\sum^{\infty}_{n=0} a_n(z-a)^n## be a real or complex power series and set ##\alpha = \limsup\limits_{n\rightarrow\infty} |a_n|^{\frac{1}{n}}##. If ##\alpha = \infty## then the convergence radius ##R=0##, else ##R## is given by ##R = \frac{1}{\alpha}##, where...

Homework Statement $$\lim _{x \rightarrow 1} (\frac{23}{1-x^{23}}-\frac{11}{1-x^{11}})$$Homework Equations i) For functions f and g which are differentiable on an open interval I except possibly at a point c contained in I, if , and exists, and for all x in I with x ≠ c, then...

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 Find \lim_{x\to \infty} \sqrt{x^2+1}-x Homework EquationsThe Attempt at a Solution This is mostly for a refresher. I know it's zero because when we multiply the top and bottom by the conjugate to obtain \frac{1}{\sqrt{x^2+1}+x} and the denominator increases without bound...

Homework Statement Find the limit \lim\limits_{t\to -1}\frac{\sqrt[3]{t}+1}{\sqrt[5]{t}+1}. Needless to say: No L'Hopital's rule, otherwise this thread would not exist. Homework EquationsThe Attempt at a Solution Have tried multiplying the fraction such that I get the difference of squares in...

Homework Statement This homework isn't for a course. There is a book on hockey physics with a section discussing puck drop below intended target. When I use the book's formula modified for drag and lift, it seems to show that a 100 mph shot, taken from 30 feet from the net, can not hit the...

If my understanding is correct the definition of a derivative is lim h->0 (f(x+h)-f(x))/h However, I've also seen this used: lim x->c (f(x)-f(x))/(x-c) are these both considered valid definition for the derivative or does the derivative have to tend towards zero? I am a bit confused because I...

Good afternoon 1. Homework Statement Draw graph of the following equation Homework Equations \frac{X-5}{X^2+X-6} = y The Attempt at a Solution my problem is searching for the vertical asymptote from what I know the way to find the vertical asymptote is by limiting the equation near to ∞...

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...

Show that $\displaystyle\lim_{p\to +\infty}C_p ((0,0); 1)=C_{\infty}((0,0);1).$ Hello, I think that this limit is infinite. At $C_p=\{(x,y)\in \mathbb{R}^2: |x|^p+|y|^p=1, \, p>1\}$, then is reasonably think. But how can show this?

Homework Statement prove: \lim_{n\rightarrow \infty} {\frac{n!}{2^n}}=\infty Homework Equations Def. of a limit The Attempt at a Solution I would like to know if my solution is right or not. I think it is right but I would like to get a feedback. Please do not give me the answer, just...

$$\lim_{{x}\to{0}}\frac{\left| 2x-1 \right|-\left| 2x+1 \right|}{x}=-4$$ I tried /x but couldn't get the answer

Homework Statement Calculate the following limit if it exists ## lim_{z\to -1}\frac{\sqrt{z}-i+\sqrt{z+1}}{\sqrt{z^2-1}} ## the branch of root is chosen to that ##\sqrt{-1}=i## Homework Equations 3. The Attempt at a Solution [/B] By inserting ##z=-1## directly, I get a ##\frac{0}{0}##...

Homework Statement Show that ##\lim _{ n\rightarrow \infty }{ \left( \frac { \sqrt { n+c } +d }{ \sqrt [ 3 ]{ { n }^{ 2 }+an+b } } \right) } =0,\quad n>-c ## Homework Equations Sandwich theorem The Attempt at a Solution Ok, So I know my method is extremely long, I'm just wandering if 1)...

$$\lim_{{x}\to{0 }}\frac{\sqrt{ax+b}-2 }{x}=1$$ Find $a$ and $b$ Clueless!

$$\lim_{{x}\to{\infty}}\frac{\sqrt{3x^2 - 1 }}{x-1}=\sqrt{3}$$ I tried dividing everything by ${x}^{2}$ but not

Consider a ##j## point all massive leg one loop polygonal Feynman diagram ##P## representing some scattering process cut on a particular mass channel ##s_i##. Invoking the relevant Feynman rules and proceeding with the integration via dimensional regularisation for example gives me an expression...

Edit: the red \E is the epsilon sign 1. Homework Statement ##Given\quad { x }_{ n }=\sqrt { n+1 } +\sqrt { n+2 } -2\sqrt { n+3 } \\ Prove\quad that:\quad \lim _{ n\rightarrow \infty }{ { x }_{ n } } =0## Homework Equations ##For\quad any\quad arbitrary\quad \E >0,\quad there\quad...

Hi, My instructor gave us a challenge problem to solve in limits: ##\lim _{ x\rightarrow \infty }{ \left[ { x }^{ 2 }\left( 1-\cos { \frac { 5.1 }{ x } } \right) \right] } ## Note that we did not take Hospital's rule yet so we couldn't have used it. Now my first thought was to use the...

Hi. I am self-studying GR and have many questions. Here are a few. If anyone can help me with any of them I would be grateful. 1 - What is the difference between Tu v and Tvu ? 2 - I have read that the order of indices matters in tensors but when transforming tensors from one coordinate...

Hello Why does Mineral Insulated heating cables have such limited power output per feet and maximum operating voltages? I thought it has to do with the dielectric strength of the MgO, that is used as an insulation in the coaxial cable, but the dielectric strength for MgO is higher than the...

Hi all! In the midst of making up limit problems to solve generally, I came across a limit in which I'm not sure of the answer. This is not homework, but merely a product of free time. Homework Statement Find the limit. ## lim_{x \to a^+} {\frac{\sqrt(a^2 - x^2)}{a}} , a > 0 ## The attempt...

I have done this problem before but forgot how to get from one step to the next: let a>0. how is absval(x^1/2-a^1/2) equal to abval(x-a)/(x^1/2-a^1/2)?

Homework Statement Given f(x,y)=(y+x)/(y-x) use an ε-∂ proof to show that lim(x,y)→(0,1) f(x,y) exists. Homework Equations |(y+x)/(y-x)-1|=|(2x)/(y-x)| The Attempt at a Solution I know that the limit is 1. I can't figure out how to massage the above any further to get it into the form...

To find the horizontal asymptotes of a rational function, we find the limit as x goes to infinity. Given the rational function ##\displaystyle\frac{x + 1}{\sqrt{x^2+1}}##, we can find the limit by multiplying the numerator and the denominator by ##\frac{1}{x}##. This gives us ##\frac{1 +...

Hi guys, I don´t understand too much the Newtonian limit of General Relativity. My question is: In this limit ga b (x) = ηa b (x) + ha b (x) where O(h2→0). Then, according to GR, it's straightforward to demonstrate that the Einstein equation Gt t = k*Tt t in that limit leads to Poisson equation...

Dear PF Forum, In previous threads, I have asked about sine and cosine. The answer given by the members/mentors/advisor are very clear. But lengthy. Perhaps these yes/no questions that I can simply remember and not forget it (again). So here we are 1. if h = 0 then sin(h) = 0 2. if ##\lim_{h...

Homework Statement The limit ##\lim_{x\to\pi}\frac{xcos\frac{x}{2}}{\pi^{2}-x^{2}}## Can be expressed as a fraction. Solve 2. Relevant equation 3. The Attempt at a Solution EDIT See new post for solution

Dear PF Forum, Continuing our debate discussion in differential in slice of X. I read this particulare website. About proofing the derivative of sine(x). http://tutorial.math.lamar.edu/Classes/CalcI/ProofTrigDeriv.aspx In there, the web writes [FONT=Courier New] arc AC < |AB| + |BC| <...

I've been trying to figure this out for days. I'm told that atmospheric pressure imposes a limit on maximum possible exhaust velocity in the Earth's atmosphere, and that under STP conditions that limit is approximately 15,000 feet per second. But that doesn't make any sense. Suppose you had...

I've read that matter and energy fields occupy all of space, and that space is integral with time, so I'm wondering whether it might be consistent with contemporary physics for undetectably small proportions of the mass of matter and / or energy to occupy arbitrarily large proportions of an...

Hi, This is a question regarding Example 3.6 in Section 3.5 (p.35) of 'QFT for the Gifted Amateur' by Lancaster & Blundell. Given, [a^{\dagger}_\textbf{p}, a_\textbf{p'}] = \delta^{(3)}(\textbf{p} - \textbf{p'}) . This I understand. The operators create/destroy particles in the momentum state...

Could someone run me through how to solve this please? I am stuck. \displaystyle\lim_{x\rightarrow \infty} {\frac{3x+5}{x-4}}

$y_0=k$ where $k$ is a constant. $x_{n+1}=30-\dfrac{y_n}{2}$ $y_{n+1}=30-\dfrac{x_{n+1}}{2}$ Prove that $(x_n, y_n)$ converges to $(20, 20)$ for all values of $k$. My attempt: I wrote a computer program and verified this for a few values of $k$. But I don't know how to prove that $x_n$ and...

Is there theoretically a smallest possible Schwarzschild radius?

Hello,Does anyone know any websites that offer limits exercise? I googled it and didn't find much, I just want limits and nothing else. Also, do limits generators exist?

What I've tried so far: $$ \begin{align*} \left |\frac {e^{x+y^2}-1-\sin \left ( x + \frac{y^2}{2} \right )}{x^2+y^2} \right | &\leq \frac {\left |e^{x+y^2}-1-\sin \left ( x + \frac{y^2}{2} \right ) \right |}{\left \| (x,y) \right \|^2} \\ &\leq \frac {\left |e^{x+y^2}-1 \right |+ \left...

Homework Statement Let ##x_n## be the solution to the equation ##\left( 1+\frac{1}{n} \right)^{n+x} = e## Calculate ##\lim_{n\to \infty} x_n## Homework Equations N/A The Attempt at a Solution Since ##\lim_{n \to \infty} \left(1+ \frac{1}{n} \right) = e## that tells me that ##\lim_{n\to...

Normally a star with a mass several times that of the sun will become a black hole at the end of the lifetime of that star. Can black holes exist with a mass much smaller than that exist? In other words, are black holes with a mass of Jupiter or even Earth exist? Or even much smaller than that...