Limits Definition and 1000 Threads

Homework Statement Show that ##\lim_{x \to a} f(x) = L## if and only if ##\lim_{x \to 0} f(x+a) = L## Homework Equations - The Attempt at a Solution For the forward direction (ie ##1 \Rightarrow 2##), I tried to first assume that 1. holds true (ie ##\forall \epsilon>0, \exists \delta>0...

Homework Statement The problem is: f(x) = {ax^2 - b / (x - 2), x < 2 1/4(x^2) - 3c, x >= 2 If f is differentiable at x=2, what are the values of a, b, and c? In case it is hard to see, I have provided an image 2. Homework Equations I know that the limit definition of a...

Hello (: Can someone help me calcultating this limit (as x → ∞) This is the function: If I just kept deriving sin(e^x) nothing really happened. So I tried using L'Hopital but partly, i guess: so: (1 or -1) × 1 + 0 + 0 / 0 + ∞ + ∞The answer must be 1 (according to wolfram alpha) but i...

Homework Statement Find the limit of the following sequence: Homework Equations \lim_{n \rightarrow + \infty} \sqrt[4] {2n + 1} - \sqrt[4] {n + 1} The Attempt at a Solution I've tried multiplying the first radical by ## \frac{ \sqrt[4] {2n - 1} } { \sqrt[4] {2n - 1} } ## to make the radical...

Homework Statement "Calculate the following limit if it exists. If it does not exist, motivate why. \displaystyle\lim_{x\rightarrow 0} {\frac{x + x^2 +\sin(3x)}{tan(2x) + 3x}} Do not use l'Hôpital's rule." Homework Equations (1) \sin(a\pm b) = \cos(a)\sin(b)\pm\cos(b)\sin(a) (2)...

Hello guys ! I need your help with the next problem: --------------------------------------------------------------------- "Show that the equation: $\dfrac{mv_0}{k}-\dfrac{m^2g}{k^2}sin\alpha \cdot ln\left[ 1+\dfrac{kv_0}{mgsin\alpha } \right]$ is equivalent to: $\dfrac{{v_0}^2}{2gsin\alpha...

Homework Statement Find the ## lim _{x-> -1+} sqrt(x^2-3x)-2/|x+1| ## Homework EquationsThe Attempt at a Solution I can only solve it using l'hopital rule and would like to know the steps of solving it without using it. ## lim _{x->-1+} (2x-3)/|1|= -5/4 ##

Hi, Suppose you want to prove |x - a||x + a| < \epsilon You know |x - a| < (2|a| + 1) You need to prove |x + a| < \frac{\epsilon}{2|a| + 1} So that |x - a||x + a| < \epsilon Why does Michael Spivak do this: He says you have to prove --> |x + a| < min(1, \frac{\epsilon}{2|a| + 1}) in...

Homework Statement Evaluate the following limit \displaystyle\lim_{x\rightarrow 4} {\frac{2-\sqrt{x}}{3-\sqrt{2x+1}}} Homework Equations lim x -> 4 The Attempt at a Solution i tried change of variables so i get √2x+1 = u then i rearranged that to get u^2-1/2 And i rearrnage original equation...

PLEASE HELP! i am so lost on this. we're using delta epsilon proofs and i am so confused since it was never properly taught to me in calc 1. find the limit. $\lim_{{(x,y)}\to{(0,0)}}\frac{x^2+y^2}{\sqrt{x^2+y^2+1}-1}$

I'm in calc 1 and want to make sure I'm understanding the reason that we find derivatives. From what I understand, a derivative is simply an equation for the rate of change at any given point on the original function. Is that correct? And the tangent line at point (x,y) is obtained by using...

Homework Statement The major problem I am facing while solving for Fourier series is about the limits to be taken while integrating..! In the general equation of Fourier series the upper & lower limits are t1 & t1+T respectively..while solving for even functions we take t1 =-T/2..! Why is it...

Homework Statement Hello, I tried to solve a problem on my own and then I looked up a solution on the web, and I realize that it seems that I goofed. The problem statement can be found at http://www.hep.fsu.edu/~reina/courses/2012-2013/phy5524/homework/solutions/hw5_sol.pdf (Problem 1, part...

Is there a way to distinguish between rational functions that have the same limit at both ends and those that don't? I think I might have answered my own question, but let's say I evaluate a rational function, and it turns out to be a coefficient ratio with no variables (3/2). Does that mean...

Hello. Let us say that we have a graph f(x)=2x when x does not equal 3, and f(x)=undefined when x=3 The limit of f(x) as x→3, is still 6. But what about the limit of 3+dx? Does it exist? I am not up to the derivatives section of my class, so maybe there is something I am not...

Hello Can someone please tell me how is: \int_{-R}^{R} \frac{\cos mx}{x^2 + 1}\,dx = 2\int_{0}^R \frac{\cos mx}{x^2 + 1}\,dx where, m and R are positive real numbers This is how I'm trying to solve it... \int_{-R}^R \frac{\cos mx}{x^2 + 1}\,dx = \int_{-R}^0 \frac{\cos mx}{x^2 + 1}\,dx...

Note, this is not a homework problem, as I'm not even in college. I just had a quick question. I know the formulas to do things such as "How many ways could you choose 5 balls from a tub of yellow, red, and blue colored balls?" (where you envision in this case, a tub where there's more than...

Hi, I am trying to derive the path length of a charged particle in a B-field. I am assuming the particle will travel a distance L along the applied field. Using the following equations for the path length of a helix and gyroradius: Helix defined as [a*cos(t),a*cos(t),b*t] for t on [0,T] has...

$$\lim_{x\to 0} \frac{x}{\sqrt{4+x}-\sqrt{4-x}}=2$$ I plotted this equation into WolframAlpha, and it applies L'Hospital and yields, for the nominator: $$\frac{dx}{dx}=2$$ I do not understand this. I have not learned how to use L'Hospital, but I know basic derivation rules, and I do...

Hello, I am facing some problem with Poincare disc. (1) How to visualize a Poincare disc? (2) The arc which runs at the end cannot be reached and runs till infinity. How does it happen?

Homework Statement If f(x) = ∫sin x0 √(1+t2)dt and g(y) = ∫3y f(x)dx, find g''(pi/6)? Homework Equations FTC: F(x) = ∫f(x)dx ∫ab f(t)dt = F(b) - F(a) Chain Rule: f(x) = g(h(x)) f'(x) = g'(h(x))h'(x)The Attempt at a Solution I tried u-substition setting u = tan(x) for the first dirivative...

Hi all, Does anyone know what physics limits human tolerance to extreme g-forces? I know the average human can take g-forces 5-7 g, and a fighter pilot, with training and a G-suit can maybe get up to 12 g. And people can survive g-forces higher than this for a very short time. I know all the...

Why is infinite kept as a lower limit in the derivation of gravitational potential energy? Shouldn't the lower limit be smaller than the upper limit? http://hyperphysics.phy-astr.gsu.edu/hbase/gpot.html

1. =\lim_{{x}\to{\infty}} (x^3+\sqrt{x^6+x^3+1} Multiplying top and bottom by x^3-\sqrt{x^6+x^3+1}, we get: =\lim_{{x}\to{\infty}} \frac{x^3+1}{x^3-\sqrt{x^6+x^3+1}} Dividing by the highest power: =\lim_{{x}\to{\infty}} \frac{1+\frac{1}{x^3}}{1-\sqrt{1+\frac{1}{x^3}}} =\lim_{{x}\to{\infty}}...

In attachments, there is a pic of a page, I think there area of sector MOA should be 2π^2/x. Please tell me how this makes sense?

Hey guys, I have a couple more questions about this problem set I've been working on. I'm doubting some of my answers and I'd appreciate some help. Question: For a, I used the subtraction limit lawto get lim g(x) and lim f(x) and subtracted the answers accordingly. Then I substituted h=...

Hey guys, I have a couple more questions about this problem set I've been working on. I'm doubting some of my answers and I'd appreciate some help. Question: So for the first one, I just used f(b)-f(a)/ b-a and got 589, 1208, and 1366 respectively via simple substitution. For 1b, I...

Prove the Sum Rule for Limits $$\lim_{x\to a} [f(x) + g(x)] = \lim_{x \to a} f(x) + \lim_{x \to a} g(x) = L + M$$ Proof Assume the following: $$\lim_{x \to a} f(x) = L, \space\lim_{x \to a} g(x) = M$$ Then, by definition ##\forall \epsilon_1 > 0, \exists \delta_1 > 0## such that...

I was reviewing some of the material in my calculus textbook when I realized that I really struggle with writing proofs. Therefore, I decided to attempt one of the easier proof related exercises found in the book. I would ask my teacher for help, but I am off for summer break. Homework...

I am familiar with the fact that the number e can be defined several ways. One particularly interesting definition is the one based on limits, namely: e = limn \rightarrow ∞ (1 + \frac{1}{n})n My question is: wouldn't it be equally true to express e as the limit of the expression above as n...

Hi there, I'm looking for some information on the current limits of the beam width of currently available lasers. I'm less interested in experimental setups that are not on the market yet, but I suppose if one of them is markedly different it would be interesting to know. Specifically...

Hi there, I'll try my best to be descriptive. I'm looking for as much information as possible on the limits on current technologies in producing copper circuitry. I had a nice conversation the other day with a member of my research group and he was telling me about the demand for the ability...

In the sense most ample and general of limits, the following identitie is true: $$\\ \lim_A \lim_B = \lim_B \lim_A$$ ?

I've been reading Brian Greene's books and he says the math for describing even the simplest physical phenomenon in the real world is wildly complex, thus physicist use vastly simplified models. Since current math is insufficient to describe everything in the universe and a final theory, will...

Proof that \lim_{x→p} \frac {f(x)}{x - p} = 0 \Leftrightarrow \lim_{x \rightarrow p} \frac{f(x)}{\left | x - p\right |} = 0 Relevant equations I think there is a useful theorem here, the conservation of signal: Suppose that \lim_{x\rightarrow p} f(x) = L ; L > 0 ; \forall \varepsilon...

Went to a tutor for help with this problem and he was stumped need to find the limit 2 - t + sin t/ t + cos t book says answer is -1 My attempts I tried two things 1. I just substituted 0 2-0 + sin(0)/ 0 + cos(0) 2/1 2 wrong answer 2. I divided everything by the...

I am having trouble solving limits with trig functions. limx→0 x+xcosx/sinxcosx useful equation limθ→0 sinθ/θ = 1 my attempt x+xcosx/sinxcosx x/sinxcosx + xcosx/sinxcosx x/sinx*1/cosx + x/sinx this is where I am getting stuck

Hi, My textbook is giving me 3 rules that must be met to be continuous: I don't understand what my textbook is trying to explain to me, - ƒ is defined at a...:confused: -Lim ƒ(x) = ƒ(a)...:confused: x→a all i undersdand is that if you draw a graph that is continuous, you must be...

Why can't EM attraction/repulsion be modeled as spatial curvature the way gravity can be? And for that matter, why can't the strong and weak nuclear forces be modeled that way either? Or can they?

Hello guys, first post here so don't get mad if I have place it in the wrong area. Going through one of my lessons earlier I was learning about the limits and fits of holes and shafts, determining the tolerances of certain objects kind of stuff. It was also briefly mentioned that you could...

Just a quick one - Have I deciphered the wording of this question properly? All necessary info is in the embedded image. To me the limits describe a typical 'pyramid in the corner', but the fact it's an integral over the function 'x' is confusing me. Do I just go with it and generate an...

Homework Statement The limit as x,y → 0 \frac{y^{2}Sin^{2}x}{x^{4}+y^{4}} Homework Equations The Attempt at a Solution There are pretty straight forward but I have a general question about them. So say in the function above I let y=x and let x approach 0. I get 0/0 -...

Homework Statement The question states: It is given limit f(x) as x->0 is 7 what should we then expect of the limit f(1/x) as x->∞ The Attempt at a Solution 0? I'm handwaving an answer because I have no idea the approach towards this problem. One states the limit x->0 and the...

Homework Statement Homework Equations The Attempt at a Solution What I don't understand is how I'm supposed to find those limits for U and V. That's not at all what I'm getting. I've tried solving for the max and min x,y coordinates from the given graphs but that doesn't yield...

Hi, I'm doing this integration: I = ∫^{1}_{-1}1/(\pi√1-x2)dx I made the substitution x = cosθ, and I'm fine with performing the integral apart from changing the limits - for x = 1 I put θ = 0, but for x = -1, how do I know whether to choose θ = \pi or θ = -\pi? The first choice gives I...

(1)If the limit of f(x), as x approaches a point a doesn't exist, and the limit of g(x), as x approaches a point a doesn't exist either, the limit of (f+g)(x) and (fxg)(x), as x approaches a point a can possibly exist? (2)If the limit of f(x) as x approaches a and the limit of (f+g)(x), as x...

I saw in a question related to Signals and systems that the limits were taken from 5- to 10+ where the signs were in the feet of the numbers..lol..i don't know what you call that. What does this mean?

Homework Statement Suppose the lim x-> a f(x) = + infinity and lim x->a g(x) = 0 then why would lim x→a (f(x)×g(x)) be insufficient to tell us anything about the product of 2 limit?

https://www.physicsforums.com/attachments/68247 I had been assigned this problem, I worked out the expansions (for practice) so they could have errors in them! I got to a point (in the photograph) where I could take out a common factor of 1/x but I'm pretty stumped although via other methods...

Justices strike down political donor limits (CNN) No need to funnel your millions through PACs any more, unless I suppose if you want to try to remain anonymous.