Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
BrighterDays
Group Title
I have the answer....I just don't understand the steps. Find the limit as x approaches infinity of 1+(a/x)^(bx)  I am putting the original question and the answer from my professor with his explanation in the comments. I just don't understand the steps at all that he has written out.
 2 months ago
 2 months ago
BrighterDays Group Title
I have the answer....I just don't understand the steps. Find the limit as x approaches infinity of 1+(a/x)^(bx)  I am putting the original question and the answer from my professor with his explanation in the comments. I just don't understand the steps at all that he has written out.
 2 months ago
 2 months ago

This Question is Closed

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
is the answer \(e^{ab}\)?
 2 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
you can guess it are you supposed to use l'hopital?
 2 months ago

BrighterDays Group TitleBest ResponseYou've already chosen the best response.0
In the comments I put a .png of how he worked it out....I don't understand his substitution with z and how he goes from there....he did say you could use l'hopital but it would be more work???
 2 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
ooh i see the solution now, sorry you are supposed to use algebra, and then the fact that \[e=\lim_{x\to 0}\left(1+x\right)^{\frac{1}{x}}\]
 2 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
the solution you have written is only algebra
 2 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
they say put \(z=\frac{a}{x}\) so the piece inside is now \(1+z\)
 2 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
that part is clear right?
 2 months ago

BrighterDays Group TitleBest ResponseYou've already chosen the best response.0
ugh. OK. so what I don't get is the algebra of: this: if z=a/b how does bx=abz^1?
 2 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
the exponential notation may have confused you lets write it without the exponential notation
 2 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
btw it is not \(z=\frac{a}{b}\) but rather \(z=\frac{a}{x}\) right?
 2 months ago

BrighterDays Group TitleBest ResponseYou've already chosen the best response.0
Oh yes, sorry  z=a/x
 2 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
ok step by step \[\large z=\frac{a}{x}\] solve for \(x\) you get \[\large x=\frac{a}{z}\] ok so far?
 2 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
multiply both sides by \(b\) you get \[\large bx=\frac{ab}{z}\] right?
 2 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
well that is it then \[\left(1+\frac{a}{x}\right)^{bx}\] becomes \[\large (1+z)^{\frac{ab}{z}}\]
 2 months ago

BrighterDays Group TitleBest ResponseYou've already chosen the best response.0
ok  I see that now.
 2 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
done right?
 2 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
or are there still other algebra steps?
 2 months ago

BrighterDays Group TitleBest ResponseYou've already chosen the best response.0
That's it! Thank you. So the fact that e= limx→0 of (1+x)^1/z is just something we need to know, correct? I keep looking for it in my book but can't find it. So, I'll just write it and make a note of it. Thanks again!!
 2 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
well i guess so usually it is written as \[e=\lim_{x\to \infty}\left(1+\frac{1}{x}\right)^x\] but if you change \(x\) to \(\frac{1}{x}\) then you get \[e=\lim_{x\to 0}(1+x)^{\frac{1}{x}}\]
 2 months ago

BrighterDays Group TitleBest ResponseYou've already chosen the best response.0
Great! Thank you so much for all your help!!
 2 months ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.