Limits Definition and 1000 Threads

Homework Statement \stackrel{lim}{y→0}\left( \stackrel{lim}{x→∞} \dfrac{\left( 1+\dfrac{ay}{x} \right)^x - \left( 1+\dfrac{by}{x} \right)^x}{y} \right) Homework Equations The Attempt at a Solution I need some hints. I really don't know how to solve these kinds of limits in which two...

Homework Statement Suppose that f' (2) = 3. Find the limit as x approaches 2 of [f(x)−f(2)]/[sqrt(x) - sqrt(2)] Answer: 6*sqrt 2 Homework Equations The Attempt at a Solution f'(x) = lim h->0 = [f(a +h) - f(a)]/h = slope [f(x)-f(2)]/ x-2 a = 2 i would think that the limit =...

Pretty general question. Integrate f(x,y,z) dxdydz over the area defined by: x^{2} + y^{2} + z^{2} \leq 4 x \leq 0 y \leq 0 z \leq 0 It is immidiately apparent that it is 1/8 of a sphere with r=2. So from that geometrical intuition we can do a variable substitution to spherical...

Hello MHB, I am currently working with a old exam and it says.\lim_{x->0}\frac{3-e^{x^2}-2\cos(x)}{x^2\sin^2(x)} and this is how far I got but struggle on the simplify Regards, |\pi\rangle

Homework Statement Have a few limits that I'm stuck on: a) lim n->infinity (n(n+1)^(n+1))/(n+2)^(n+2)) b) lim n->infinity (n^n/(n+3)^(n+1)) c) lim n->infinity n^(-1)^n I've tried my best to understand what to do solve these, but can't get it. We've been given answers to standard...

Homework Statement Homework Equations The Attempt at a Solution Are my limits of integration right?

Homework Statement Use sandwich Rule to find the limit lim n> infinity (a_n) of the sequences, for which the nth term, a_n, is given. Homework Equations ^{lim}_{n\rightarrow∞}\frac{n!}{n^{n}} The Attempt at a Solution I know by just looking at it, n^n Approaches infinity much...

Calculus 2: Sequence Limits Question to the power n?? Homework Statement Find the limits (if it exists) to decide which sequences, whose nth term is given below. Homework Equations (\frac{3^{n}-4^{n}}{3n^{2}+4^{n}+7}) The Attempt at a Solution I've done a few of these but as Soon as the...

When calculating the limit of the function f(x) = (x^2 + 3)/ sqrt(2x^4 + 5) as x→∞, is it correct to square the top and then place the resulting polynomial under a square root (i.e. sqrt(x^2 + 3)^2)? Then you can rewrite the problem as the square root of the limit as x→∞ of the resulting...

Homework Statement X is uniformly distributed over [-1,1]. Compute the density function f(y) of Y = 2X2 + 1. Homework Equations The Attempt at a Solution FY(Y) = P(Y < y) = P(2X2 + 1 < y) = P(X < +\sqrt{1/2(y-1)} = FX(+\sqrt{1/2(y-1)}) We have that f(x) = 0.5 for -1 < x <...

Here is the question: Here is a link to the question: Maths: Caluclus > Functions? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

I have the expression: limb->-8[½b^2]-limb->8[½b^2] Is it rigorously defined how to calculate this? The question arose because I want the additivity of improper integrals to work and if you take the integral of x from minus infinity to infinity to work the expression above must be zero.

Homework Statement I need to find the volume of the region bounded by (x-1)^2 + y^2 =1 \ \ \text{and} \ \ x^2+y^2+z^2=4 \ . But I only need help setting up the limits of integration. Homework Equations The typical cylindrical change of variables. The Attempt at a Solution I have 0 \leq...

Hello, I was studying the theorem of smoothness/compactness in Fourier theory and at the very last step of the proof one gets the result that \omega F(\omega)\to 0 when x\to \infty. The author of the book writes this result in little-o notation as: \omega F(\omega) = o(|\omega|^{-1}) which I...

I'm in analysis and I'm trying to understand the following. Homework Statement g(x) = integral from 0 to x+δ of f(x)dx + integral from x-δ to 0 of f(x)dx g'(x) = f(x+δ) - f(x -δ) So how do they get g'(x)?

Homework Statement Let ##x_k=k## for ##k \leq 31## and ##\displaystyle x_{k+1}=\frac{x_1+x_2+...x_k}{k}## for ##k \geq 31##. Also let ##y_k=x_k## for ##k \leq 31## and ##\displaystyle y_{k+1}=\frac{y_k+y_{k-1}+...y_{k-30}}{31}## for ##k \geq 31##. Now if ##z_k=y_k-x_k## for all ##k ε N##. Find...

Homework Statement Why is it that when using the comparison theorem my limits of integration must be from a constant value to infinity and not from negative infinity to infinity? For example ∫ x/(1+x^2) dx from -∞ to ∞

Hi, all. I'm trying to ascertain whether it is remotely possible for a human being to survive acceleration from 100 to 7000 mph (essentially, from 0 to Mach 10) in say 5 seconds? 10 even? Assume the mass that of an ordinary man, and perhaps a co-pilot, the vehicle probably a prototype of modern...

I received permission from my father to post this from his (unpublished) Calculus text. Note that this method will, I believe, work for proving existence of a limit for a nonlinear function at any point that is not a local extremum. My father thought it would be good to give you this proviso...

Homework Statement Prove that ##\lim_{x \rightarrow a} f(x) = \lim_{h \rightarrow 0} f(a+h)##. Homework Equations By definition, if ##\lim_{x \rightarrow a} f(x) = l## then for every ##\epsilon > 0## there exists some ##\delta_1## such that for all x, if ##0<|x-a|<\delta_1## then...

∞ ∫ x/(x^2+1) dx -∞ I basicaly evaluated the integral and Ln (x^2+1) as the antiderivative and when taking the limits I get ∞-∞ (ln |1| -ln|b+1|) + (ln|n+1|- ln|1|) lim b-> neg. infinity lim n-> infinity does this function converge or diverge? this was a question on...

Homework Statement evaluate the integral 1/(u^2 -36) from 0 to 6 does the integral converge? Homework Equations The Attempt at a Solution integral 1/(u^2 -36) integral 1/((u-6)(u+6)) Partial fraction decomposition 1/((u-6)(u+6)) = A/(u-6) + B/(u+6) 1=A(u+6) + B(u-6) 1=(A+B)u +(6A-6B) A+B=0...

So say I have an arbitrary function and I want to know it's limit as x,y approaches 0. I could test what happens when the x-axis approaches 0, y-axis as it approaches 0 but there are some functions where I'm told that I also need to test what happens when y=mx approaches 0, and then y=x^2 and...

Hello guys, I am stuck in page 129 on Calculus Vol I - Apostol book. I would like to know if there is anybody here who can help me. I am not a mathematician, so It might be a simple transformation but I am not going through it. He states that: lim(x->p) f(x) = A is equivalent to say that...

I have the following integral: \int_0^{f(x,y)}{f' \sin(y-f')df'} Now suppose that f(x,y) = x*y, my question is how do I write the integral in terms of x and y only? Can I do something like this? Since df=\frac{\partial f}{\partial x}dx+\frac{\partial f}{\partial y}dy we can obtain...

Homework Statement a. lim x→0 (x^3 − 2x + 7)/(3x^2 − 3) b. lim x→-1 1/(x+1) Homework Equations The Attempt at a Solution For a. I obtained a limit of 7/-3 For b. the limit does not exist (I really unsure about this)

Hi guys, I've been on quite a random change of variables binge lately and I've been messing around with a particular scenario in which I'm not 100% sure of how I should choose my limits of integration. Any help would be greatly appreciated! (And no, this is not homework, etc.) The scenario is as...

Homework Statement ∫e-Sxsin(ax) dx, S and A are constants, upper limit is ∞ lower is 0 Homework Equations ∫ u dv = uv - ∫ vdu The Attempt at a Solution After integrating by parts twice I got: (S2)/S(S2+a2) lim c→∞ [-sin(ax)e-Sx + acos(ax)e-Sx] |^{C}_{0} Okay, now how on Earth do I take...

I was fiddling around with the definition of limits at infinity and believe I have found a statement that is equivalent to the definition. So the question is this: are the following two statements equivalent? (1) \lim_{x\rightarrow\infty}f\left(x\right)=L (2) \exists c>0\exists...

Homework Statement The maximum deflection of a beam is given by the equation y=M/P(sec(μL/2)-1) μ=√(P/EI) Where EI Is a constant. Show that as P→0 y→ML^2/8EI This is a mathCAD problem by the way, but I'm very novice at it so i want to try formulise some sort of solution on paper...

Homework Statement This is not really a homework or a coursework question. But I got a warning that I should submit my post in this section of the website.. I'm just saying this because I don't know if the answer to my question is at all achievable. And if it is how I should go about trying to...

Could someone look over this and see if I have any mistakes? I'm trying to show that ∫ y' dx = ∫ dy through definitions. http://imgur.com/6zCHYo5 Thanks!

I'm not entirely sure on the properties of limits, but this seems to work. Could someone look over this for me? http://imgur.com/6zCHYo5

I want to show that if f(x) > g(x) \forall x \in (-\infty, \infty) and \displaystyle\lim_{x\to\infty}g(x)=\infty , then \displaystyle \lim_{x\to\infty}f(x)=\infty . This result is true, correct? If so, what theorem should I use or reference to show this result? I wasn't sure if...

I have a few questions for my homework assignments for solving limits, but in order to do those questions I have to use a few standard limits that we haven't been taught, which means I'll have to prove them. I know these can be done using L'Hopital's rule, but we haven't covered that yet so I...

(Hey guys and gals!) Homework Statement Given a bounded set x_n and for any y_n the following condition holds: \limsup_{n \rightarrow ∞}(x_n+y_n) = \limsup(x_n)+\limsup(y_n) Show that x_n converges. Homework Equations Definition of limsup(x_n) = L: \forall \epsilon > 0 \mid...

I'm trying to find the integration of my function f[x] from 1 to 4 using the indefinite integral and inserting limits using rules. I am not sure how to insert the limits with rules, have been playing about with the following Integrate[f[x], x] /. x -> {1 >= x <= 4} which ain't working, any...

Homework Statement Evaluate the limit of each indeterminate quotient: lim (x-->4) [2-(x^1/2)]/[3-(2x+1)^1/2] Homework Equations The Attempt at a Solution The answer in the book is 3/4. This MAY be wrong though. My attempt: I basically tried rationalizing the numerator AND denominator but...

Homework Statement we have this function f(x)=1 if \frac{1}{x}\in Z ( aka integer) f(x) = 0 otherwise Prove that limit (as x approach 0) dosen't exist (use the definition of limit - trying to prove that limit as x approchaes 0 and x approchs 0+ will not work here)<-- hint given by the...

lim e^(1/(6-x)) x->6+ Was wondering how to solve for this limit analytically. I plotted it and see it going to 0, but that is not the answer in the book.

A panel put out over 30.7 volts, say 34 volts and I have a micro-inverter that require a voltage of 11-30 to work. Other than shading some of the panel, is there a way to half the voltage from the panel without as much loss from shading some of the cells to work the inverter?

Homework Statement lim x->4 (1/((sqrt x)-2))-4/(x-4) Homework Equations The Attempt at a Solution I have made several stabs at this problem. First I tried using values very close to 4 (e.g. sqrt of 4.001) Then I tried rationalizing the expression 1/((sqrt x) -2). That did...

(Hello everyone!) Homework Statement Given that \limsup_{n \rightarrow \infty}(\frac{1}{x_n})\cdot \limsup_{n \rightarrow \infty}(x_n)=1 Show that x_n converges. Homework Equations Recalling that: x_n \text{ converges } \iff \liminf(x_n)=\limsup(x_n) The Attempt at a Solution Started with...

What are the inner and outer limits of the habitable zone in distance for the sun?

what is physical and geometrical meaning of limits?

Homework Statement Just checking if these are right? f(b) = 2-2√b compute limit in are as: b-> 0+ b->1- Explain in a brief sentence why it does not make sense to compute a limit as b->0- Homework Equations given above The Attempt at a Solution lim b->0+ (2-2√b) = 2...

I have a list: 85 45 75 60 90 90 115 30 55 58 78 120 80 65 65 140 65 50 30 125 75 137 80 120 15 45 70 65 50 45 95 70 70 28 40 125 105 75 80 70 90 68 73 75 55 70 95 65 200 75 15 90 46 33 100 65 60 55 85 50 10 68 99 145 45 75 45 95 85 65 65 52 82 Sorry for the poor formatting, but I created a...

I'm familiarized with finding limits of most kinds of functions. I was struck by a problem: What if the variables of the function belong to different sets of numbers? My point being, given the function: f(n,q)=\frac{n}{q} With n belonging to the set of natural numbers and q belonging to the...

Homework Statement I was trying to prove something and I ended up in a situation similar to, (limit t\rightarrow0)(limit s\rightarrow0) f(x+s,y+t) =(limit s\rightarrow0)(limit t\rightarrow0)f(x+s,y+t) My question is when does this equality hold. I can't find it anywhere...

Homework Statement Suppose the functions f and g have the following property: for all ε > 0 and all x, If 0 < \left| x-2 \right| < \sin^{2} \left( \frac{\varepsilon^{2}}{9} \right) + \varepsilon, then \left| f(x) - 2 \right| < \varepsilon. If 0 < \left| x - 2 \right| < \varepsilon^{2}...