# x&gtinfinity

1. ### lim x->infinity (1+(1/x))^x

Hi, I have another question on limits: lim (1+(1/x))^x x->infinity So i assume that I have to use L'Hopital's Rule to get to an answer Firstly I have let y=the equation and taken the natural log of each side: ln(y)=ln[(1/(1+(1/x)))^x] and then made it the form...
2. ### Limit x->infinity

So this is a diffrent that i got no clue what to do next because i it got highest Power on top not dominator (on bottom on divide) limit x->infinity x^4+x^5 so i multi by (x^4-x^5)/(x^4-x^5) after some simplifie i get (x^8-x^10)/(X^4-x^5) and now i shall divide both with x^5 and at bottom i...
3. ### Limit x->infinity

Hello im stuck with a question limit x->infinity (sqrt(x^2+ax)-sqrt(x^2+bx)) Picture show My progress

I've to prove that as we take the limit of cosine as x goes to + infinity, the limit DNE. I've looked on different forums and sites, but all have methods I barely understand. I'm not very familiar with the Delta-Epsilon definition of limits. I've tried to look at the sticky at the top and try to...
5. ### Epsilon-proof as x->-infinity currently defeating me

I think Epsilon-delta proofs and I should spend some quality time together. The problem is I need to prove that: \lim_{x \to -\infty} a^x = 0 So, I need to show that, for every \epsilon > 0, there is a \delta such that |f(x) - L| < \epsilon whenever x < \delta. So, given \epsilon > 0, I need...
6. ### lim (1+1/x)^x as x->infinity

Good afternoon, I am working on a problem that asks to find the following limit: lim_{x\rightarrow\infty}(1+\frac{1}{x})^x This should be equal to e, but I am having some difficulty remembering why. I checked WolframAlpha and was provided with the following...
7. ### Finding the limit of ((x-1)/x)^x as x->infinity

Dear all, I am trying to find, analytically, the limit of ((x-1)/x)^x as x->infinity. I tried l'Hopital's rule but it seems to make it more complicated. I know that the limit is 1/e but need to show my working and understand why it is 1/e. Hope you can help! Many thanks Mike
8. ### Limit as x->[infinity]

lim(n->[infinity]) (1+(1/n))^n = ????
9. ### Limit of ln(x+1) as x->infinity

Hi, I'm a bit rusty on my math since it is summer... but i have to do this summer assignment. The original question is which of the following functions has a horizontal asymptote at y=-1? and it lists like 5 equations, one which is y=ln(x+1) I'm thinking that you have to find the limit as...