Limits Definition and 1000 Threads

Homework Statement Find \int^{2}_{1}x^{-2}dx. Hint: Choose x^{*}_{i} to be the geometric mean of x_{i-1} and x_{i} (that is, x^{*}_{i} = \sqrt{x_{i-1}x_{i}}) and use the identity \frac{1}{m(m+1)} = \frac{1}{m} - \frac{1}{m+1} The Attempt at a Solution First off I am very confused by...

Homework Statement I have a limit problem, however I do know how to work limits, I guess what I need is more of a refresher on how to work third degree polynomials. The polynomial(s) I am trying to work with are the following: x3-2x2+2x-15 -and- x3-5x2+10x-12 The limit is a limit where x...

Can anyone suggest me a self study book for limits and continuitsy whic starts from zero level to a very advanced level thanks in advance rithu

i guys, I'm stuck on wording of a homework assignment and thought you might be able to help me. There are several questions... Consider the geometric series: (Sum from k=0 to infinity) of ar^k and consider the repeating decimal .717171717171 for these problems: Question 1: Find a formula...

Homework Statement Interpret the integrals (from 0 to 4)∫ (3x/4) dx + (from 4 to 5)∫ (sqrt(25-x^2)) dx as areas and use the result to express the sum above as one definite integral. Evaluate the new integral. Homework Equations The Attempt at a Solution I see that I could...

Okay so I've been teaching myself (with the aid of the mighty internet & several friends) algebra & now calculus. I have found that I didn't do too good at high school for various reasons. Some good...some not good. Anyway... I have a (what is probably a basic question) about factoring limit...

Homework Statement My professor gave us this problem: Convert the limit to an integral: \lim_{n\rightarrow inf} \frac{1}{n}(\sin(\pi/2) + \sin(\pi/2) + ... + \sin(\pi)) he said it was right endpoint from [0,π] then he set Δx = \frac{\pi}{n} then \lim_{n\rightarrow inf}...

Hi, If k_3 \cdot (A_1 \cos k_1 x + A_2 \sin k_1 x)\cdot(B_1 \cos k_2 y + B_2 \sin k_2 y)\cdot(C_1 e^{k_3 z}-C_2 e^{-k_3 z})=E in the limit as \sqrt{x^2+y^2+z^2}\rightarrow\infty Can we infer anything about any of the constants?

I'm trying to design my first switching regulator circuit. I require three voltage rails, 5V, 3.3V and 1.8V. But to get started, I'm just focusing on 1.8V. I've decided to use the LT3507 as it seems to be commonly available here. It also has 3 buck regulator outputs, so it's a one-chip solution...

Homework Statement Find volume bounded by: x - z = 0; x + z = 3; y + z = 1; z = y + 1; z = 0 Homework Equations Vol = \int\int\int_{V}dV The Attempt at a Solution I really don't know how to begin this problem because I have trouble visualizing what all those intersection of...

Homework Statement The Attempt at a Solution When I do the integral of this function I'm unsure of what the limits are. Anyone care to help? Thanks

http://img827.imageshack.us/img827/4765/img0161u.jpg I don't know how to integrate e^(t^2) like that. I am thinking that it become e^(t^2+1) with some constant in front of the whole expression. And then with A) I just don't know how to begin. A kick in the right direction would help...

! SOLVED ! This isn't a homework problem, just an equation in my chapter. I don't see how the two integrals pointed to by the blue arrows become the integral pointed to by the red arrow. I know that if you swap the limits of integration, you change the sign of the integral. However, how do...

Homework Statement evaluate the limit as x approaches 0 of (sin(2x))^3/(sin(3x))^3 Homework Equations The Attempt at a Solution the answer in the textbook is 8/27 i figured they got that by raising 2 to the 3rd and 3 to the 3rd but I'm not entirely sure what happens to the...

Homework Statement The question asks to use the squeeze theorem to show that the limit of n!/n^n equals 0 as n approaches ∞. Homework Equations I need to use the squeeze theorem to solve this problem, and I'm not sure what the upper limit is. The Attempt at a Solution I found...

Good Morning, I am working on a project that is designing a water pump for a car engine without any mechanical parts (works on waste heat building pressure to circulate the water). I know that most of the car engine heads are aluminum and that blocks are part cast steel and part aluminum. In...

Homework Statement lim(x -->0) (1-cos(14x))/(xsin(18x)) Homework Equations None? The Attempt at a Solution The hint tells me to use L'hopital's rule through which I got lim(x-->0) (sin(14x))/(18xcos(18x)+sin(18x)) (I factored out the 14 in the numerator) That gave me a 0/0 so I did...

1. Is the universe finite? 2. Could it be just the surface of a higher dimensional object? 3. If something travels across the universe will it reach the same point? 4. Could the effects of the accelerating universe, that scientist credit dark matter to, be just a side effect of some...

Homework Statement integrate modulus of xcos∏x within the limits -1 to 1/2 P.S I'm not allowed to use acaluculator so graphing and finding out the answer not possible Homework Equations it's using the property of definite integral ∫f(x) dx within the limit from a to b = ∫f(x) dx...

How can you tell if a limit does not exit or that it goes to infinity? examplelim\underbrace{x\rightarrow}_{0}(\frac{\sqrt{x+1}}{x}) The x goes to 0The book says the limit is \infty but if you take the left side limit you get -\infty and if you take the right side of the limit you \infty. So...

I've worked all of these out. I'm mostly confident I did them correctly, but I'm prone to overlook subtleties or counterexamples sometimes. http://i111.photobucket.com/albums/n149/camarolt4z28/1ab-1.png http://i111.photobucket.com/albums/n149/camarolt4z28/1gf2-1.png

Show that, with t\in [0,1] : \lim_{n\to\infty} \frac{\sin(nt)}{n}=0 This is easy but I've forgotten how to calculate limits. Can anyone jog my memory?

Homework Statement Prove or disprove: if lim x->b (from the left) f'(x) = infinity then lim x->b (from the left) f(x) = infinity Homework Equations my gut instinct is that this is false. The Attempt at a Solution I have thought of many counterexamples but none of them seem to...

Help with the Formal Definition (ε-δ) of limits! Hey, I am in Honors Calc 1 in college and I have this take-home graded worksheet on Epsilon-Delta for limits and it's killing me. I have to prove that lim(x^2+3x+5)=3 as x->-2. So far I have: For any given epsilon>0 there is a delta such that...

Hi guys, Starting revision for my exams and I can't seem to solve these problems. ): 1. Given that three non zero vectors A, B and C are perpendicular to each other and that the vector R = pA + qB + rC is a zero vector, show that p = q = r = 0 2. In another question, given that f(x)...

I am skeptical that strong human-like AI is possible. I think AI can be made to look very much like human intelligence but I don't think it will actually be like human intelligence in the way that you and I are. For example, I don't think a computer can Actually feel pain or pleasure or fear and...

Homework Statement Consider a force-free particle of mass m described, at an instant of time t = 0, by the following wave packet: \begin{array}{l} 0 \ \mathrm{for} \ |x| > a + \epsilon \\ A \ \mathrm{for} \ |x| ≤ a \\ -\frac{A}{\epsilon} (x − a − \epsilon) \ \mathrm{for} \ a < x ≤ a + \epsilon...

In all the problems I have done so far, the limit was already given. So the goal is to utilize the theorem to see whether the limit really holds. But what's the point? If we already know how to find the limit, why must we go through a process of ingenuity algebra to tell ourselves, "okay it...

Homework Statement lim \underset{x \rightarrow }{\infty} {\frac{1+t^2}{1-t^2}}i+tan^{-1}(t)j+\frac{1-e^{-2t}}{t}k First term = =\frac{1/t^2+1}{1/t^2-1}=-1 How do I show the second term and also the e^(-2t) term? Thanks

Does Ohms Law have practical limits? For example:A piece of steel wire of length of length 10um and of CSA 20E-10. Can we calculate the resistance of such a tiny piece of wire (resistor) in the usual way? thanks

Homework Statement I'm just trying to find liminf and limsup for: Homework Equations E_n = (n, n+2) The Attempt at a Solution Since every subset occurs a finite number of times, would I say that limsup is the empty set? Is being bounded by nothing the same thing as being bounded by...

Homework Statement The limit as x approaches 2^+ of (x-4)/(x-2) The limit as x approaches 2^- of (x-4)/(x-2) Homework Equations The Attempt at a Solution Figured out that the domain is x ≠ 2, therefore 2 is a vertical asymptote not sure where to input values/what to do really..

I spent a lot thinking of this but can't fingure out how to find the limit as it approach x=64 Plz need help :) F(x) = (sqrt(x)-8)/((x)^(1/3)-4) find f(x) lim x->64 also this question - lim x-->0 ((x+1)^(1/3)-1)/((x+1)^(1/4)-1) Thanks in advance

I'm trying to teach myself maths, and I have a couple of problems I can't figure out. 1. \lim\sum\limits_{k=1}^{n}\frac{2k-1}{2^k}. I see that this is =\lim\sum\limits_{k=1}^{n}\frac{k}{2^{k-1}}-1 but I have no idea what to do with that. I tried writing it as...

I need help with this question. I understand that logic behind it; as P approaches O the value the right bisector Q reaches it's maximum. I don't know how to show this algebraically however. Help?

Homework Statement The actual numbers aren't completely relevant. I made a graphic. http://i168.photobucket.com/albums/u193/kamikazehighland/calculus.png I'm actually not in calculus or engineering. I'm actually writing a program, but I've done enough research to know how to...

Homework Statement I am doing self-study. I am on problem 5.6 #27 in the Stewart text 3rd E. I don't understand why the integration limits changed after the given substitution. The given substitution was: x=θ^2 dx=2θdθ Homework Equations Please see attachment. The Attempt at...

1. Homework Statement , is best expressed in the photograph, as this is a fairly detailed problem: [PLAIN]http://img833.imageshack.us/img833/3972/pleasehelp.jpg 2. all equations included in the image 3. the attempt at the solution is in the image as well When I take the limit of that last...

f(x)= ((cosx)^{2}+1)/e^{x}^{2} So for the limit of f(x) as x→∞ I would just input ∞ for x. I'm confused after this though, wouldn't it just be ∞/∞ = 1? the next part says show that there exists a number c ε (0,1) that f(c)=1 I don't know what this is asking for me to solve.

This is an assignment problem I have. Can't seem to figure it out. It has two parts, one to prove that the function approaches 0 where y=mx and and one where the function approaches 0 from y=kx2... f(x,y) = (x3y)/(2x6+y2) I've attempted both parts and get stuck on what seems like the same...

Homework Statement [b]1. I'm trying to figure out how to take limits involving i and complex functions f(z) The first problem is as follows: lim(n \rightarrow \infty ) n*((1+i)/2))^n The second is: lim (z app. 0 ) of (sinz/z)(1/z^2) The third is: lim (z app. e^i*pi/3) of...

Homework Statement \lim_{\substack{x\rightarrow 2\\y\rightarrow 2}} f(x,y)=\frac{2x^2+2xy+2x-xy^2-y^3-y^2}{2x^3-2x^2y+2x-x^2y^2+xy^3-y^2} Homework Equations N/A The Attempt at a Solution Well, I tried using the line y = 2, and let x approach 2 (as well as making x=2 and let y...

1) = 0 The denominator grows much faster than the numerator. 2) = 0 Each of these terms would simply be zero, right? For 4) and 5), the f(x) = x3 I simplified these to 4) = [(x-2)(x2+2x+4)]/(x-3) 5) = [(x-3)(x2+3x+9)]/(x-2)...

Homework Statement Find a value for k to make f(x) continuous at 5 f(x)= sqrt(x2-16)-3/(x-5) if x cannot equal 5 3x+k when x=5 Homework Equations none The Attempt at a Solution lim x->5 sqrt((x+4)(x-4))-3/(x-5) * sqrt((x+4)(x-4))+3/sqrt((x+4)(x-4))+3 lim x->5...

Homework Statement Evaluate the following limits or determine that the limit does not exist. b) lim (x,y)–>(0,0) (1+xy)^(1/xy) Homework Equations The Attempt at a Solution I have a funny feeling this limit might exist. (Then again I get that feeling about every indefinite...

Question: Guess the oblique asymptote of the graph f(x) for x→∞. Write down the limit you have to compute to prove that your guess is correct. f(x)= \sqrt{(x^{4}+1)/(x^{2}-1)} so the limit would be: lim x→∞ \sqrt{(x^{4}+1)/(x^{2}-1)} I sketched out a graph but I just have no clue how to...

I have 2 questions in regards to continuity and limits. Question 1: f(x)= e^{-x^{2}} if x ≠ 0. f(x)= c if x=0. For which value of c is f(x) continuous at x=0? I was thinking the answer would be 1 but I feel that's incorrect. Question 2: Compute lim x→∞f(x). I'm not familiar with how to...

Homework Statement The problem is: A function in the form of f(x)/g(x) is given: [x^2 - pi^2/4 ]/tan^2(x) as x \rightarrow pi/2. Homework Equations The Attempt at a Solution Surely I can't solve this question using L'hopital's theorem since it's applicable to indeterminate...

I'm not sure about my work. N = neighborhood N* = deleted neighborhood c = accumulation point http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20111011_224646.jpg http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20111011_224704.jpg

I am having a little problem finding the limits of integration to this conv. just for the sake of fulfilling my curiosity. Although it is stated in the textbook but I can not do the actual integration and get the same results!f(x) := \begin{cases} 1 & if \ 0<x<1 \\ 0 & otherwise \end{cases}...