Limits Definition and 1000 Threads

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

My question is: Show the limit of x_{n}=\frac{ln(1+\sqrt{n}+\sqrt[3]{n})}{ln(1+\sqrt[3]{n}+\sqrt[4]{n})} as n approaches infinity Solution: {x_n} = \frac{{\ln (1 + {n^{\frac{1}{2}}} + {n^{\frac{1}{3}}})}}{{\ln (1 + {n^{\frac{1}{3}}} + {n^{\frac{1}{4}}})}} = \frac{{\ln \left(...

Homework Statement Find the general solution of the given differential equation, and use it to determine how solutions behave as t→∞. y' − 2y = 3et Homework Equations DE The Attempt at a Solution After some work, I got y=-3et+ce2t . Now I have problems in getting the...

so solving lim's can be tedious not because they are hard but because you have to continously keep writing lim x->a while solving the equation is there a mathematical shortcut to writing limits without keep writing lim x->a all the time after each development? thanks.

Homework Statement Find the general solution of the given differential equation, and use it to determine how solutions behave as t→∞. a) y' − 2y = t2e2t Homework Equations DE The Attempt at a Solution After doing the linear DE steps I end up getting y(t)= t3e2t/3 + ce2t...

Homework Statement 1. Calculate lim x->0 (xtanx/cos(2x)-1) without using L'Hospitals rule.Homework Equations I am told that lim x->0 (sinx/x)=1 The Attempt at a Solution If I substitute 0 in it gets 0/0. I have tried several trig identities without luck.

Homework Statement Suppose ##f(x)## and ##g(x)## \rightarrow 0 as x \rightarrow 0+. Find examples of functions f and g with these properties and such that: a.) ## \lim_{x\rightarrow 0+} { f(x)^{g(x)} = 0 } ## Homework Equations None The Attempt at a Solution Let ## f(x) = 2^x-1...

Homework Statement lim of (a^x-a^-x-2)/(x^2) as x->0 Find the value of the limit^. The answer is (lna)^2 I know how to get the answer using L'Hospital. However, I do not want to use Hospital's rule. I think I see the pattern with the special limit: lim of (e^x-1)/x as x->0 But I...

Hi, I am in a first semester Calculus I course in college with an intermediate skill level with precalc and a basic understanding of limits and infinity. I do not understand how to solve this problem I attempted to do so only to find out after completion that ∞/∞ is indeterminate rendering my...

Consider the following lim f(f(x)) x->-2 When looking at the graph of a function, if the function approaches -2 from above on the right side, and approaches -2 from below on the left side, does the limit exist? I've been told it doesn't, but I don't understand why.

Ok, so I'm not really too good at group theory and that kind of math, so I hope I can explain my question: I tried to evaluate \frac{d}{dx}e^{x}: \frac{d}{dx}e^{x} = \frac{e^{x+h}-e^{x}}{h}, h -> 0 = \frac{e^{x}e^{h}-e^{x}}{h}, h-> 0 = e^{x}(\frac{e^{h}-1}{h}), h-> 0 So I figured...

Homework Statement The function f is defined on a neighborhood N of \bar{x}. Show that \lim_{x \rightarrow \bar{x}} f(x) = L if and only if \lim_{n \rightarrow \infty} f(x_n) = L when \{x-n\} is a sequence of points in N with \lim_{n \rightarrow \infty} x_n = \bar{x} . Homework...

Homework Statement I need to prove that 1/n has a limit of zero using the following definition: The statement that the point sequence p1, p2, . . . converges to the point x means that if S is an open interval containing x then there is a positive integer N such that if n is a positive...

When is the following equivalence valid? $$\lim_{x \to a} f(g(x)) = f(\lim_{x \to a} g(x))$$ I was told that continuity of f is key here, but I'm not positive. This question comes up, for instance in one proof showing the equivalence of the limit definition of the number e to the...

First of all, I have to use all the limit laws I can to get these answers correct as the prof said. 1) lim (3x^3 + 2x^2) x->1/3 I factored out x^2, put the x^2 in front of the limit(constant multiple law), plugged in 1/3 into the x's, then multiplied everything together and got 1/3 for my...

I have a question about complex valued functions, say f(z) where z=x+iy is a complex variable. Can every such complex valued function be represented by: f(z)=u(x,y)+iv(x,y)? Also, is the limit of the conjugate such a function equal to the conjugate of the limit of the function? Something like...

When the limit of a function turns out to be infinity ,how should we interpret it ? For ex. we have \lim_{x \to 0}\frac {1}{x^2} = \infty What does this mean ? Does it mean that the limit is ∞ or does it mean that the limit does not exist as ∞ is not a number ? I would appreciate if...

Homework Statement lim x→∞ ##\frac{7x^2 + x + 11}{4 - x}##Homework Equations The Attempt at a Solution I am sorry I am posting so much. But I think I have learned two different ways to compute limits at infinity of functions: one by the math lab tutor and another by the professor, but I am...

Homework Statement Find the limit and any horizontal asymptotes: lim 4/(e-x) x→∞ Homework Equations Principle 1: A limit defines a horizontal asymptote whenever x→∞ or x→-∞. Principle 2: If a limit goes to ∞ or -∞, there won't be a horizontal asymptote. The Attempt at a Solution lim...

Here are the questions: I have posted a link there to this topic so the OP can see my work.

Homework Statement Given that lim f(x) = 4 x → 2 lim g(x) = -2 x → 2 lim h(x) = 0 x → 2 find the limits that exist for the problems below. If the limits do not exist, explain why.c) lim √f(x) x → 2 e) lim (g(x)/h(x)) x → 2 Homework Equations lim √f(x) x → a = √(lim f(x)) x → a and...

Hi all. I'm trying to come up with a way to determine if the defectivity of a particular widget is 'different' to the usual defectivity of a widget. The difficulty comes from the fact that widgets are made in batches of 25. We'd like to investigate any widgets which have a higher (or lower)...

I'm going to talk with someone at a local university tomorrow to see if I can get out of AP Calculus. Essentially, I would like to be prepared for our meeting tomorrow. I'm good with integrals, so that shouldn't be a problem. However, I'm not quite as confident with derivatives, limits, and...

I know this is probably a dumb question, but I have a question regarding this. My textbook says the following: "A function f is differentiable at a if f'(a) exists." It then follows with and example regarding if f(x) = |x| is differentiable at x = 0. They prove this by finding the limit of its...

Hi, sorry for the quite long text. Thanks in advance for any help! I am a little confused about the different limits in which the AdS/CFT correspondence is conjectured to hold in its stong, intermediate, weak form. I am trying to understand the correspondence motivated by Maldacena's...

Don't really know how to get round this, the -1^n confuses me. Homework Statement Determine whether the following sequence {an} converges as n→∞? if it does, find limn→∞an Homework Equations an=(3n+(-1)n )/ (n3+2) Homework Statement

When a particle decays into two different particles, they are said to be entangled. If one of these is absorbed by an atom or there is a subsequent interaction with another particle, what happens to the previous or initial entanglement? Does it diminish or completely go away? For example...

I am trying to get a head start and learn some calculus before my class begins this fall. I'm trying to learn from Khan Academy, but I'm already confused. I thought the definition of a limit was a value that could never be reached, though could be infinitely close to being reached. Here is a...

So I'm trying to study for my calc 3 exam, but I have noticed that my book doesn't have many limit questions that use sin/cos/tan, but I know those will likely be on the test. I have tried to google but I can't find many examples that have solutions. Are there any free sites that have problems...

My question is that why is their a need for both upper and lower while calculating Definite Integrals. The question arose when i thought of Definite integration as something related to Differentiation. Or is it that only Indefinite Integration is directly related to differentiation. In...

I'm interested in reading about the fundamental limits imposed by known physics on distorting spacetime in ways that bring two masses closer together so that speed of light travel time between them is reduced. I'm familiar with the concept of inflation theory. I think of it as a rapid...

Homework Statement source: http://tutorial.math.lamar.edu/Classes/CalcI/DefnOfLimit.aspx

I have been trying to learn calculus by my own, but when it comes to proving limits I get very confuse. Could somebody explain me what is being done here? If you know any resources that could help me with this task let me know. here is the source...

Homework Statement Find \lim_{x\rightarrow \infty} (\sqrt{x+\sqrt{x+\sqrt{x}}}-\sqrt{x}) Homework Equations The Attempt at a Solution Rewriting the given expression, \sqrt{x}\left(\sqrt{1+\sqrt{\frac{1}{x}\left(1+\frac{1}{\sqrt{x}}\right)}}-1\right) What should I do with the...

Hi everyone, I am having a 'crisis of faith' in how the limits of an integral should change when you make a substitution for the variable involved. Especially when using a sinusoid substitution, since the sinusoidal functions are not 1-to-1 functions. Anyway, let's use an example integral...

Homework Statement Integrate (1 + x2)1/2 from -∏ to ∏ Homework Equations The Attempt at a Solution I substiuted x = tan(theta) but when I went to change the limits of integration I got 0 and 0. What am I doing wrong?

Lets say that we have two Cauchy sequences {fi} and {gi} such that the sequence {fi} converges to a limit F and the sequence {gi} converges to a limit G. Then it can easily be shown that the sequence defined by { d(fi, gi) } is also Cauchy. But is it true that this sequence, { d(fi, gi) }...

Homework Statement So I keep evaluating these limits wrong. Something is wrong in my thought process. Homework Equations http://www.calcchat.com/book/Calculus-ETF-5e/ chapter 9, section 1, question 69 Consider A_n = (1+k/n)^n If I wanted to see if it converged or not I would just...

Are there limits to exposure to microwave frequency power within a certain range, for example with workers on a transmission tower? What would be the applicable standards? I understand that RF is non ionizing radiation, but I have read that high power RF radiation can cause burns if too...

Hi, I was wondering if some one could check my understanding of limits please. If a limit is presetned as say x << y or x >> y am I right in thinking that x or y can be ignored as they are small enough to be insignificant? So, for example, if I had equation which was sin(x/y) in...

Homework Statement ##\int_{2}^{\infty} ue^{-u} du## The Attempt at a Solution What I did was find the family of functions described by the indefinite integral ##\int ue^{-u} du## then found the limit as b increases without bound. $$=\lim_{b\rightarrow \infty}...

Hi all, I was wondering what factors determine axial resolution in spherical lenses. I know that axial resolution in conventional light microscopy at least is about half as good lateral resolution. I've read about the huygens-fresnel principle of diffraction and how this can account for the...

Homework Statement Given that f(x)= x* ((ln x)^2) f'(x)= ((ln x)^2) + 2 ln x f"(x)= (2 ln x) (1/x)+ (2/x) (a) find the intervals on which f(x) is increasing. (b) find the intervals on which f(x) is concave up. (c) find lim f(x) as x-> +∞ and lim f(x) as x -> 0+ Homework Equations The Attempt...

Homework Statement Use theorems to find the limit: \lim_{x\rightarrow 1} \cos(arctan({\frac{\sin(x-1)}{x-1}})) Homework Equations Theorems like f(x)=c is continuous f(x)=x is continuous \lim_{x\rightarrow 0} \cos(x)=1 \lim_{x\rightarrow 0} \sin(x)=0...

Find a function (or several or all) f(x) which satisfied all these three conditions: (1) lim [x→∞] f(x)/aˣ = 0 if a ≥ e (2) f(x)/aˣ → ∞ when x→∞ if 0 < a < e (3) lim [x→∞] f(x)1/x = e.

Lim(x-->0) x/a[b/x] can be written as x/a(b/x-{b/x}) how can we write this as lim(x-->0) (b/x -b/a({b/x}/{b/x}))?

ℂI am working on an assignment and have come across a question that I'm not quite sure how to approach. Here it is, with my "solution" and reasoning: "[F]ind the limit at ∞ of the given function, or explain why it does not exist. 24. h(z) = Arg z , z \neq 0" (Complex Variables Second...