What is Limits: Definition and 1000 Discussions

Homework Statement an= (n/n+2)^n The Attempt at a Solution I was told this was convergent and I need to find the limit of the sequence. How do I do this, as I seem to keep getting that this is divergent. Isn't it divergent to infinity? Or am I missing something?

Is there a "Leibnitz theorem" for sums with variable limits? Wikipedia says that if we want to differentiate integrals where the variable is in the limit and in the integrand, we can use Leibnitz theorem: But what if I need to integrate a function defined like this:\Sigma_{I(x)}[f(x,t)]...

\int (x+1/x2-3x-5)dx I can't put the limits on the integral sign, 5 is the top limit and 3 is the bottom limit. I can solve using partial fractions ok but I have never solved with limits before. Where do the limits come in, do I need them at the start or can I factorise as usual and use...

Homework Statement Calculate the limit, if it exists: lim x→3+ = 81-x4/(x2-6x+9)2 Homework Equations The Attempt at a Solution -(x4-81)/(x-3)(x-3) = -(x2-9)(x2+9)/(x-3)(x-3) = -(x-3)(x+3)(x2+9)/(x-3)(x-3) = -(x+3)(x2+9)/(x-3).....I'm stuck here and don't know what to...

Homework Statement By considering different paths, show that the given function has no limit as (x,y) \rightarrow (0,0). f(x,y) = x4/(x4 + y4) Homework Equations The Attempt at a Solution My instructor taught me this process a while back and am unsure if it fits for this...

Hello, I have seen (in H Cartan's differential calculus) a proof that if F is a Banch space, L(E,F) where E is some vector space, is also a Banach space. One of the main points of the proof is based on the behaviour of a function being "proper" (continuous) on a ball of arbitrary radius "n"...

is the upper limit always greater than the lower limit in integration? what should be the limits if we need to calculate total work done in bringing a mass from infinity to distance r from earth.

Homework Statement Evaluate \iint\limits_S \vec{A} . \vec{n} ds over the plane x^{2}+y^{2}=16, where \vec{A}=z\vec{i}+x\vec{j}-3y^{2}\vec{k} and S is a part from the plane and R was projected over xz-plane. Homework Equations Surface Integral and Double Integration.The Attempt at a...

So I have this question: And I just want to check my answer. Am I right? I think that the first formula is the theorem of integration so a and b are limits o integration and I'm not sure about the second formula, I think it's the anti derivative formula making that the anti derivative...

Hi everyone, I've the equation x+y=6 (it's a surface equation which I'll integrate over) and the following integral limits is what I suppose to get it from the equation: \int\limits_0^6 \int\limits_0^{6-x} What's the trick here?

Problem statement What is the left hand and right hand limit of 1/x^2 -4 at its vertical asymptote? Revelant equations None Attempt at a solution It's vertical asymptote are 2 and -2. I have attached my work . I understand it however at the back of the book it says the left hand limit at...

Homework Statement Integrate the following over the set E. \int_E \frac{2x+y}{x+3y} dA Bounded by the lines: y = −x/3+1 y = −x/3+2/3 y = −2x y = −2x + 1 Homework Equations None. The Attempt at a Solution I can up to the same point everytime, but always get stuck on finding the new...

A limit of a sequence is definitely convergent if: If for any value of K there is an N sufficiently large that an > K for n > N, OR for any value of K there is an N sufficiently large that an<±K for n > N My only question is what exactly are K, N, an and n? What values are they? How would...

1. what would be the limit?? without using the L'Hopital's rule lim_(x-0) (sin(3 x^2))/(8 x) the limit of sin(3x^2) divided by 8x as x approaches zero 2. Limits of trignometric functions 3. The Attempt at a Solution I tried factoring out the 1/8, but...

Homework Statement Let f be the function defined by $$ f(x) = - ln(x) for 0 < x ≤ 1. $$ R is the region between the graph of f and the x-axis. http://learn.flvs.net/webdav/educator_apcalcbc_v10/module08/imgmod08/08_10_01.gif b. Determine whether the solid generated by revolving region R...

Hello, I am struggling with limits in my calculus course and would appreciate a bit of help. The question is: \lim_{x→-6}\frac{x^2-8x+12}{x^2-x+30} So far I have tried the factoring and substitution methods but have not managed to match the answers given by online equation solvers. For...

Homework Statement ∫∫ydxdy over the triangle with vertices (-1,0), (0,2), (2,0) Homework Equations I did it like this and got the right answer: ∫dy ∫ydx this first: ∫ydx from x = (y-2)/2 to x = 2-y then ∫dy from y = 0 to y = 2 I got 2 which is correct but when I...

When do you check the limit from the right and left of a limit with an absolute value in the numerator or denominator? For example, why do you check the limit from both sides of: Lim x -> 3/2 (2x^2-3x)/absolute value(2x-3) But only the left side of: limit as x approaches -2...

Hi! Here is my task: Here is my attempt of solution: Does it make sense? How should I find limits for u and v? I appreciate any help!

1. $$f(x)=x-\frac{1}{6}x^2-\frac{2}{3} lnx$$ Homework Equations limits The Attempt at a Solution I know there is a vertical asymptote at x=0 because all values of x have to be greater than x. The answer says that there is no horizontal asymptote, but I don't know how it...

I am trying to check whether lim h→0 (R(h)/||h||) =0 or not. I am working in ℝ2. h=h1e1+h2e2** => ||h||=(h1^2+h2^2)^1/2 I am using the definition that (R(h)/||h||)<ε * whenever 0<|h|<δ for all h. Example 1 (R(h)/||h||)=h1h2/(h1^2+h2^2)^3/2 I can see that the denominator dominates...

I am trying to show {fn} converges uniformly on {z:|z|≤p}, where p is postiive real number. and fn(z)=sin(z/n). I am able to follow parts of my books method, but don't understand a couple of the inequalities...(my trouble lies in the inequalities rather than the main concepts involved in the...

Knowing that the limits of integration of a any function, for example: \int_{-\infty}^{+\infty}\delta (x)dx=1 I know that's correct call your primitive through the limit superior as a variable, so H(x)=\int_{-\infty}^{x}\delta (x)dx But, and if I want to describe your primitive through the...

Homework Statement evaluate the following limits if it exist lim x sin1/x and limit x sin 1/x x→0 x→∞ Homework Equations The Attempt at a Solution Someone have told me that I should let t=1/x and rewrite the limits.However, once I rewrite the...

I believed the definitions of derivative that we know was really definitions f'(x_0)=\lim_{x\rightarrow x_0}\frac{f(x)-f(x_0)}{x-x_0} f'(x_0)=\lim_{\Delta x\rightarrow 0}\frac{f(x_0+\Delta x)-f(x_0)}{\Delta x} But not, is one definition, just use the equality bellow in equations above... \\...

Homework Statement 1. lim as n approaches infinity of ((n+1)^5-(n-1)^5)/n^4 2. lim as n to infinity (n!)^2/(2n)!Homework Equations The Attempt at a Solution 1.I split it up, got (((n+1)/n)^4)*(n+1)-(((n-1)/n)^4)*(n-1). I try to simplify that down to (n+1)-(n-1) and got 2 as my answer, since the...

lim x--> 1 \frac{x^4 - 3x^3 + 3x^2 - x}{x^4 - 2x^3 + 2x - 1}I got \frac{0}{6} = 0

Need someone to check my work.lim t -> 0 \frac{e^{2t} - 1}{1 - cos(t)} after I took the derivative twice I got \frac{2}{0} = undefined?

so in the image in the link below, i don't understand a couple of things: 1.) the center of the cylinder is off to the side and not at the center. where/how in the problem are we taking this into account? because it should definitely affect the volume under the parabaloid right? 2.) most of...

hi , i have a problem that i couldn't solve , i know its limit should be 1 because i looked up in the helping part of my manual . i must calculate : LIM (when n goes to infinit) ( (n^2 + n + 1) * ln( (n+1)/(n+2) ) * ln ( (2n+1)/(2n+3) ) ) i know i should use the case of 1 ^ infinit but i can't...

Homework Statement I am to explain all intercepts, critical numbers, extrema, inflection points, and asymptotes of the function f(x)=(x-4)/x^3. 2. The attempt at a solution a) The y-intercept does not exist, as the domain of the function is all real numbers except x=0. Solving the...

Homework Statement http://i.minus.com/jJQzZXoxXFqEB.png Homework Equations (b-a)/n = Δx The Attempt at a Solution I know how to express the sum as an integral .. almost. It is the integral of cos(2+x) with respect to x. However, what are my bounds of integration? I know that b-a must...

Homework Statement Let ##\displaystyle a_n=\frac 1 2+\frac 1 3+...+\frac 1 n##. Then A)##a_n## is less than ##\displaystyle \int_2^n\frac{dx}{x}##. B)##a_n## is greater than ##\displaystyle \int_1^n\frac{dx}{x}##. C)##\displaystyle \lim_{n\rightarrow \infty} \frac{a_n}{\ln n}=1##...

First of all, THIS IS NOT HOMEWORK. It's related to my research. And forgive me if this is rather elementary (sadly, I was something of an underachiever at school, which has left some gaps in my maths education that I've been working on since I returned to education) but I have a question...

i'm trying to integrate some some function bounded by the x-y domain of x2+y2=6y which is a circle on the x-y plane shifted upward where the outer part of the circle is 6. i'm trying to integrate a double integral.. ∫∫f(x)rdrdθ i don't know how to express my limits of integration for r...

Homework Statement http://i.minus.com/iCJwlfzPc5fRu.png Homework Equations This feels like a movie requiring the suspension of disbelief. The Attempt at a Solution cot(x) = cos(x)/sin(x). cot(0) = 1/0 Right? How in the world then is 0cot(0) - 1 = 0? That should be infinity minus 1.

removable discontinuity Homework Statement the following function f(x)=(4-x)/(16-x^2) is discontinuous at? i got at -4 but some of my friends say its 4, -4 how is that possible

1. lim θ→0 \frac{sinθ}{θ+tanθ} Homework Equations lim x→0 \frac{sinx}{x}=1 lim x→0 \frac{cosx-1}{x}=0 The Attempt at a Solution lim θ→0 \frac{sinθ}{θ+sinθ/cosθ} lim θ→0 \frac{sinθ}{(θcosθ+sinθ)/cosθ} lim θ→0 sinθ × \frac{cosθ}{θcosθ+sinθ} lim θ→0 \frac{θcosθ}{θcosθ+sinθ}...

hi all, I have following integral and i was wondering if i can manipulate limits to simplify it. ∫^{t}_{0} P(τ) exp( - a ∫^{t}_{τ} P(u) du) dτ I know that the answer is \frac{1}{a} - \frac{1}{a} exp( - a ∫^{t}_{0} P(t) dt) But don't know how to get there. Thanks in advance.

Homework Statement Find the limit, using L'Hospital's rule, if appropriate. lim lnxtan(pix/2) x->1^+Homework Equations The Attempt at a Solution http://imgur.com/gbhQutU I've done this question and gotten the correct answer by making lnx the numerator and 1/tan(pix/2) the denominator, but...

I know I am already boring with limits,but i again have two of them to deal with and i don't know how... 1. \lim _{n \to \infty} \frac{5^{n^+1}-2*5^n+5^{n-1}}{3^{n+1}-3^n} 2. \lim _{n \to \infty} \frac{\sqrt[3]{n^4}+\sqrt{n}+1}{\sqrt[6]{n^4}+\sqrt[3]{n}+2}

Again i have two similar problems: \lim _{n \to \infty} \frac{3n-\sqrt{4n^2+n}}{3n+\sqrt{4n^2-n}} \lim _{n \to \infty} \frac{\sqrt{9n^2-n}-2n}{\sqrt{9n^2-n}+2n} Those kind of problems will be on my exam,which is very close,and i don't get it how to deal with this limits... I just say...

Everything here is in a Hilbert space. If x_n\to x and y_n\to y in norm, then under what conditions does <x_n,y_n>\to <x,y>? Is this always true, and why? Does anyone have a source?

Hopefully this is in the right sub-forum. Anyway, we all know the Planck length placed a limit on how small something can be and still make physical sense. Is there a macro version of this? Is it possible that the universe/multiverse, or some other macro object, can only be so big before it...

when we find a limit for an undefined point on a curve , X^2 - 1 / x - 1 at x = 1 for instance we reshape the equation without actually changing anything to find the limit at this point . why can't we do that to define the point on the function ? i mean clearly if we say F(x) = x^2 - 1 / X -...

If you have f(x) = 1/x and g(a) = (cosx - 1)/x and then y = [limx→0 f(x)][limx→0g(x)], the two individual limits equal 0 and infinity, respectively. Since these are limits and only approach these values, would the multiplication of the two limits equal 0, infinity or something else?

Homework Statement Consider a function f: D∈R, where D = {1/n for natural numbers n (1, 2, 3, 4, etc.)} and f(x) = 3x - 1 for all x in D. Explain why the limit of f(x) as x → 1 does not exist. Homework Equations The Attempt at a Solution Uh I figured it would exist. We know a...

Homework Statement Hi. I have a problem finding the limit of two different problems - without use of l'Hôpital's rule. I only know how to do this with use of the l'Hôpital's rule, therefore I'm seeking help to solve this problem.Homework Equations The problems are: Determine the limits...

Homework Statement lim x->1 (X^9 + x -2)/(x^4 + x -2) I know how to do this using L'Hopitals Rule and I get 2 Homework Equations (1+b)^n = 1 + bn + n(n-1)b^2/2! + n(n-1)(n-2)b^3/3! ... The Attempt at a Solution Let x = h+1 x -> 1 h -> 0 lim h->0 (h+1)^9 +...

Homework Statement lim x-> ∞ xsin(1/x) Homework Equations The Attempt at a Solution I know that this is an ∞.0 type limit but I can't figure out how to change the sin function. Thank you