Limit Definition and 999 Threads

Let f(x,y) be defined by f(x,y) = [x2y2]/[x2y2 + (x-y)2] a) Find the domain of the function f. b) show that (0,0) is a boundary point of the domain of f c) Compute the following limit if it exists: lim (x,y) ---> (0,0) f(x,y) The Attempt at a Solution a) I first change the value (x-y)2 to...

I have to find this: $$\lim_{{x}\to{3}}\frac {\sqrt{6x - 14} - \sqrt { x+1}}{x-3}$$ So I do this: $$\lim_{{x}\to{3}}\frac {\sqrt{6x - 14} - \sqrt { x+1}}{x-3} * \frac{\sqrt{6x + 14} + \sqrt{x+1}}{\sqrt{6x + 14} + \sqrt{x+1}}$$ The top part is easy since $$(\sqrt{a} - \sqrt{b})(\sqrt{a} +...

Homework Statement Evaluate lim h->0 ((8+h)^⅓ -2)/h. Homework Equations Hint: Let 8+h=x^3The Attempt at a Solution I've uploaded a picture of my calculation. But I am not sure if that is the final answer or is there a following step to get the answer.

Hello there, Plack law of radiation $$ B(\nu) = \frac{2\,h\,\nu^3}{c^2(e^{h\nu/kT}-1)} $$ I want to show that for small frequencies, Reyleigh-Jeans law: $$ B(\nu) = \frac{2\nu^2kT}{c^2} $$ is correct. I take the limit of Planck law as ##\nu \to 0## using l'hopital rule: $$ \lim_{\nu \to 0}...

I am reading some papers about astroparticle physics and I see something like Parker limit (monopole). So what is the purpose of setting up this limit ? It is be used to get the expected number of particles per unit area per unit time for later experiments ? Thanks

Homework Statement Lim (cos^2(t))/(t^2+1) t->∞ Homework Equations squeeze theorem -1<=Cosx<=1 The Attempt at a Solution I have -1<=Cos(t)<=1 (-1)^2<=Cos^2(t)<=(1)^2 (1)/(t^2+1)<=(Cos^2(t))/(t^2+1)<=(1)/(t^2+1) I took both of limits of the 2 outsides as t->0 i got -1...

Homework Statement So this is part of a broader problem about the quantum harmonic oscillator, but there's one particular bit of mathematics I'm stuck on. We have the differential equation: y''(x) +(ε-x2) y = 0 And I'm told that we're to examine how y behaves as x tends towards...

so suppose i have a wire given parametrically by C(t)=x(t),y(t),z(t), and i run a current of I amps through it. to find the total B field i would sum up the contributions over the length of the wire, and (please tell me if I am wrong) the total B field due to the wire at point p=xp,yp,zp would...

Prove that $\lim_{{x}\to{0}}\frac{1}{x^4}=\infty$, given a $M>0$ So we need to prove that $f(x) > M$: $\frac{1}{x^4}>M$, $\frac{1}{M}>x^4$, $\frac{1}{M^{1/4}}>|x|$ Is that right so far? Is the absolute values necessary in my last statement?

Hello Folks, I am solving a limit proof that has the following attached solution. Question: Assume all sn ≠ 0. and that the limit L = lim abs(sn+1/sn) exists. Show that if L<1. the lim sn=0 I Understand the solution except for one part which is also attached.. sn = sN*sN+1/sN*** sn/sn-1 Can...

Say we have a function that is defined as y=3 except at x=2 and 5 where there are two vertical asymptotes. would this function have a two sided limit? what if I were to take the limit when x approaches 3? would that be y=3?. what about one sided limits? If I were to take the positive limit as x...

So I've been trying to solve this limit problem for some time. Here is the problem:- \lim_{x\rightarrow 0} {\frac{6sin(x) - 2sin(3x)}{tan^3(3x)}} I cannot use l'hopital's rule to solve it. I've tried taking 2 as a factor, then trying to use a trig identity, but I couldn't figure a...

Let $I$ be an interval and $A_{n}$ be the set of $k/n$ where $k$ is an integer. Prove that $|I|$ is the limit as $n$ tends to infinity of $\frac{1}{n}|(IA_{n})|$ where $IA_{n}$ denotes intersection. My plan was to split it up into cases for the different type of intervals and come up with...

Homework Statement Estimate the instantaneous velocity of a particle with position function s(t) = 2t2−4t at t = 1 using the four intervals [0.9, 1], [0.99, 1], [1, 1.01], and [1, 1.1]. 2. The attempt at a solution At t=1, y = -2 Slope of a line: a = (y2 - y1)/(x2 - x1) = (y2 +...

Homework Statement Show that lim(n→infinity) 1/n*{2*4*...*2n/(1*3*...*(2n-1))}^2 exists without finding the limit. Homework Equations probably the following: Let {xn} be a sequence such that xn≥xn+1 and xn≥M for every n. Then the series is convergent. The Attempt at a Solution I know...

Definition of 'Limit of function (f) at x=p' Let E be domain of f and p be a limit point of E. Let Y be the range of f. If there exists q∈E such that for all ε>0 there exists δ>0 such that for all t∈E for which d(t,p)<δ implies d(f(t),q)<ε. Then we say that f(t)->q as t->p. 1) Suppose f...

Suppose we are given the function $y=2+\frac{1}{x^2}$. Prove that given $x>\frac{1}{(\epsilon)^{1/2}}$, where $\epsilon > 0$, then $2- \epsilon < y < 2 + \epsilon$. So the first part is easy: $$x>\frac{1}{(\epsilon)^{1/2}}$$ $$x^2>\frac{1}{\epsilon}$$ $$\frac{1}{x^2}<\epsilon$$...

Today was our first lesson in our high school's accelerated calculus class. The class is our school's most second most difficult math (behind multivariable calc), and prepares you for the AP BC calc exam, but material not present on the BC test is covered in class. It is really a college level...

Homework Statement Lim ( 5+6x2)/(√(x3)) + 2x2 +1) x->∞ Homework Equations not allowed to use lhopitals rule The Attempt at a Solution first, i divided by x2, which yielded (5/(x2) + 6 + √(x)) / (2 + 1/x2 ) then i assumed that thelim x--> infi of 5/x2 = 0, lim x-->...

Homework Statement limx->∞ e^5x/ln(2x) Homework Equations The Attempt at a Solution

Homework Statement lim x->0 (2sinxcosx)/ (2x^2 + x ) Homework Equations 2sinxcosx = sin(2x) The Attempt at a Solution denom. factors to x(2x +1) how to proceed?

Hi all, I'm just beginning calculus and I'm having trouble figuring this one out. I need to solve this one without using l'hospital's rule. Homework Statement Find Limit (sin(4x)/sin(6x)) as x->0 Homework Equations We know that limit (sin(x)/x) as x -> 0 equals 1...

Homework Statement lim x->0 sin4x/2x Homework Equations lim x->0 sinx/x =1 The Attempt at a Solution can I write lim x->0 sin4x/2x as sinx/x * 4/2 = 1*2 or am I missing a step ?

Homework Statement lim x->0 sinxcosx/x Homework Equations lim x->0 sinx/x = 1 The Attempt at a Solution Pretty sure I need to use above property but I believe cosx/x is undef.

Homework Statement limx->64 (x^1/3 - 4)/(x - 64) Homework Equations The Attempt at a Solution (64^1/3 -4)/(64 - 64) = 0/0 = not defined

I'm having trouble with this limit. It gets complicated really quickly when I apply l'hopital's. Any hints? $$\lim_{{x}\to{a^+}}\frac{\cos\left({x}\right)\ln\left({x-a}\right)}{\ln\left({e^x-e^a}\right)}$$

I kind of know what limits are, or at least believe I do: I think that a limit of a sequence is just an approximation/intuitive way to finding a number (if it exists) to which a sequence tends. For example, 1, 2, 3, 4... tends to +∞, while 1/10, 1/100, 1/1000... tends, "obviously/intuitively"...

Hi (Wave), back already :D For what values of $a$ and $b$ is the following equation true? $$\lim_{{x}\to{0}}\left(\frac{\sin\left({2x}\right)}{x^3}+a+\frac{b}{x^2}\right)=0$$ I tried l'hopitals rule, but it just got more complicated. My progress...

I'm working through some problems from Stewart's Calulus, 6ed. and am having some difficulty with certain limit proofs. In particular, there is no definition provided for limits of the form: $$ \lim_{x \to - \infty} f(x) = L $$ One of the exercises is to come up with a formal definition...

Homework Statement find limit ##\lim _{ x\rightarrow \infty }{ \frac { { 10 }^{ x } }{ x! } } ## Homework Equations l'hopitals rule The Attempt at a Solution on substitution we get ##\frac { \infty }{ \infty } ## on using l'hopitals rule,what is the result of differentiation of x!? or...

Homework Statement Apply the definition of the limit to show that \begin{align*} f(x,y) = \frac{x^2\,y\,\left( y - 1 \right) ^2 }{x^2 + \left( y-1 \right) ^2 } = 0\end{align*} I know I'm required to use the epsilon delta method here, no polar stuff either, just straight at it. Homework...

Homework Statement How do you determine if the limit of (1+1/n^2)^(n^2) exists and what it is? This cannot use logarithms at any point. Homework Equations (1+1/n)^n --> e The Attempt at a Solution Let N=n^2 Given (1+1/N)^N --> e, then (1+1/n^2)^(n^2) must --> e also. Is...

Homework Statement I'm referring to the question and solution for part (b) in the attached TheProblemAndSolution.jpg file. Homework Equations Definition of limit. The Attempt at a Solution Should the equation with the two things in brackets have absolute value bars instead of brackets...

Homework Statement lim x --> 0 for function y = (-2x)/(sinx) Using L'Hopital's Theorem, I found the derivative of the top and of the bottom and found the limit and got -2. How to find the limit as x approaches 0 without using L'Hopital's theorem. I know my solutions manual uses a...

So I am in the process of building various solenoids for some projects I have. But the issue I have is that the battery I use is over heating. From my understanding, when I connect a circuit to a battery, the energy gets dumped very quickly and overheats the cell. Is there a way to calculate how...

Hey guys, this is a question that has been bothering me since I finished my special relativity course last year. I was told that nothing can travel faster than the speed of light. Thinking relativistically, I take this to mean no one thing in the universe can travel faster than any other...

Homework Statement lim x --> 0 for the function sqrt((1/x^2)-(1/x)) - sqrt((1/x^2)-(1/x)) Analyze the cases x > 0 and x < 0 The Attempt at a Solution The solutions book simplifies the expression to 2x/(abs(x)*(sqrt(1+x)+sqrt(1-x))) I know how to evaluate the limit from here. But I'm...

Hey guys, Here's another quick question this time from a problem set I'm having trouble with at the moment. Question: So, for a, I computed f(x) = x^5 This is because of the numberator's right side. If 2+h is raised to the 5, this must be the function. Moreover, a=2 because 2 is already on...

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 1a, I just took \lim_{{h}\to{0}} of the function using [ f(x+h)-f(x) / h ] and simplified. Ultimately, this gave me...

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=...

Hi to everyone. I'm new on here (in fact, this is my really first message). I need some help with the next limit, I hope you can help me: $$\lim_{x \to \infty} \sin (x\pi\sqrt [3] {x^3+3x^2+4x-5})$$ Thank you so much for your time! :)

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is there any other way to find the limit on 58(b). its on page 3 of the link. http://www.math.uga.edu/~clayton/teaching/m115f09/homework/hw2solutions.pdf

Homework Statement This problem is found in a chapter about rational functions in my review book. The expression is as follows: \lim_{x\rightarrow a} {\frac{2 x^2 + 5x - 3}{x - a}} = \ \text{L} where 'a' is a constant. I'm supposed to find a value of 'a' that allows the limit to...

hi fellas, I have been working on Chandrashekhar limit, and I found a mass-radius relationship for the nonrelativistic fermi gases using this formula and i got the graph of this R=((18pi)^(2/3))/10 *H^2/(GmM^(1/3) ) (0.5/n)^(5/3) where H=(6.63*10^-34)/2pi G=6.67*10^-11 m=9.11*10^-31...

Hi, I'm having trouble understanding the following fact about limits : If f(x)<=g(x) for all x on (a,b) (except possibly at c) and a<c<b then, lim f(x) <= lim g(x) x -> c x->c Here's how I interpret the definition : We have two functions f(x) and g(x), and the inequality f(x)<=g(x)...

I think i discovered a new way to define an integral, i don't know if it helps in any particular case, but its an idea worth posting i think. The idea is to define the height of the rectangles based on one single point of the function and then build up the next heights for the other rectangles...

Suppose ##\lim_{x \to a} f(x) = \infty## and ##\lim_{x \to a} g(x) = c## where ##c## is a real number. Prove ##\lim_{x \to a} \big( f(x)+g(x) \big) = \infty##. Proof Assume ##\lim_{x \to a} f(x) = \infty## and ##\lim_{x \to a} g(x) = c##. Then, by definition: 1) For every ##M > 0##...

I am looking for some assistance in creating a way to stop a skid steer loader that drives on a confined course if it hits the wall. We currently operate a theme park where children drives skid steers loaders and we have a remote E-stop. the course is enclosed and surrounded by a barrier system...