# infinity

1. ### L'Hopital's Rule on an Absolute Value function. Two different answers?

Suppose there is a function, k, which is equal to . Now suppose I take the limit as n approaches infinity, so that . Now, I am at a crossroads. Do I: A)keep the absolute value bars and simply evaluate the limit of the function inside them? Or; B)remove the absolute values since we know...
2. ### Limit of Infinity

limit -x^5 + x - 1 as x goes to infinity Can I add infinity? -(infinity)^5 + infinity - 1 = -infinity + infinity (is it now positive or negative infinity?)
3. ### Limit of Infinity for Exponential Absolute Function

Find the indicated limit. lim as x goes infinity of |(x + 1) / (x - 2)|^(x^2 - 4)^(1/2)
4. ### Does Not Exist Limits

Can I answer DNE limits as infinity or negative infinity? like this lim sin(x) as x goes to infinity = infinity? lim sin(x) as x goes to -infinity = -infinity?
5. ### Infinity Limit - Trigonometric Function

Find horizontal and vertical asymptotes. (a) f(x) = tan x/(1 - sin 2x) (b) f(x) = cot(1 - cos x) For the vertical asymptotes it is easy to determine them (a) pi/4 (how to find the rest of angles in general?) is it pi/4 + npi? (b) 2pi But the horizontal asymptotes it is difficult because...
6. ### Limit Involves Sine as x goes to Infinite

Find the limit of the following functions as x goes to Infinity. (a) f(x) = sin[ (x^2 + 4) / (x^2 - 4) ] (b) f(x) = (4 sin x)/x
7. ### limit of x going to positive infinity (cos(1/x))

IDK how to do the problem limit of x going to positive infinity, where f(x)= (cos(1/x)) ( we cannot use the chain rule; we have not learned it yet). only thing I would do is just plug in positive infinity for x. So what is cos 1/ positive infinity?? Is there any other way to do this problem...
8. ### Epsilon-Delta Question (Limits at Infinity)

I'm having trouble with these kind of Epsilon-Delta questions. I cannot find these kind of questions anywhere on the internet. If you know a website that can teach me this, please do so. My final is in two days so please help. These kind of questions are my only problem. Thank you.
9. ### Summation n = 1 to infinity (-1)^(n+1)*(2+(-1)^n)/n convergence or diverg.?

Hello, I need to find out if summation n = 1 to infinity (-1)^(n+1)*(2+(-1)^n)/n is convergene or divergence. Lim n = 1 to infinity (n+1)*(2+(-1)^n)/n = 0, so we don't know for sure. What's the best way to check if it's convergence or divergence?
10. ### New thought experiment with infinity - circles with infinite points inside them

(sorry, I don't know in which section I should post this question) I now think I have some idea why Cantor (or whoever it is) said things like "there are more real numbers R than whole numbers N." So I think I've understood the concept of comparing infinite sets. And why this is...
11. ### Converges or diverges? 1 / (n * (ln n)) from 2 to infinity

Hello, Can you help me understand why the back of my textbook says this converges? I got that it diverges, and I'm trying to understand where I went wrong. Σ 1 / (n * ln (n)) from 2 to infinity I think that this series is continuous, decreasing, and results in positive terms from two to...
12. ### Summation n=1 to infinity (sqrt(n+2)-2*(sqrt(n+1))+sqrt(n))

I'm having a little trouble making this work. The equation is summation n=1 to infinity (sqrt(n+2)-2*(sqrt(n+1))+sqrt(n)), any help? According to Wolfram the answer is 1-sqrt(2)
13. ### Comparison test - f(x) = x / (x^3 + 1) from 0 to positive infinity

I need to see if the following is convergent or divergent. f(x) = x / (x^3 + 1) [0, + infinity) I tried creating a function that was larger than this. I came up with g(x) = x / x^3 = 1 / x^2 The issue is that when I take the limit of g(x), I end up with ( -1 / t ) - ( -1 / 0...
14. ### Limits at infinity

I'm trying to calculate the limit by dividing the numerator and denominator with the highest t exponent, then using lim 1/x^n = 0 x->∞ Can someone help? Stewart Calculus , vol 1 , 2.6; n20 lim (t - t√ t) / ( 2t^3/2 +3t -5) t-> ∞ Thanks.
15. ### Setting a constant to infinity

I was fiddling with the Dirac wave equation the other day and derived a very simple solution: the free particle wavefunction, otherwise known as a "plane wave." The question isn't about the derivation but the arbitrary constant. The a comes from the usual separation of variables: I separated...
16. ### limit of absolute values at infinity

Hello, I am having trouble with this limits question: Evaluate (abs(-x)+abs(3-x))/x as x tends to infinity I know the answer is 2 but I can't seem to solve it. It would be of great help if you could explain it step by step, I would greatly appreciate it!
17. ### There are different sizes of infinity right?

I was curious about infinity, and I asked my teacher a question. The question originally started of as why 0.9999... = 1. (I know that they are equal, but I wanted some clarification on it) I showed him lim_{n\to\infty}\frac{x+1}{x^{12}+1} \Rightarrow \frac{\infty}{\infty} We all know that...
18. ### Limit at negative infinity?

So my roommate asked me a question for a limit problem, and he said they haven't learnt L'Hopitals Rule yet. The problem is as follows: IM NOT SURE HOW TO WRITE NEGATIVE INFINITY IN LATEX, SO I ONLY PUT INFINITY. ALL THE LIMITS SHOULD BE READ AS THE LIMIT AS X APPROACHES NEGATIVE INFINITY...
19. ### Limit: Sum to infinity of reciprocals of factorials with alternating sign

Hello, I'm a bit stuck on this and would value your help please. I know that the sum to infinity of the reciprocals of factorials is e. But what if they have alternating sign, e.g. 1/1! - 1/2! + 1/3! + 1/4! - ... I have found the answer: identity (9) at...
20. ### limit of (x)^(1/x) as x approaches infinity using l hopital rule

limit of (sqrt rt (x^2 + x)- x ) as x approaches infinity using l hopital rule i managed to gt sqrt rt ( ∞² +∞)-∞ , which is also equal to ∞ , but the ans given is 0.5 , how to do that ?