A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
i need help finding the limit of the sequence
(1 + 1/n) ^ n using l'hopitals rule
anonymous
 5 years ago
i need help finding the limit of the sequence (1 + 1/n) ^ n using l'hopitals rule

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the limit as n goes to infinity I assume?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I understand taking the ln of it so you get n ln (1+1/n) then you have ln(1+1/n) / 1/n but then i am lost

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you almost did 75% of the problem

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now you're ready to apply the l'hopital's rule, that's taking the derivative of both The numerator and denominator

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so the denominator would be 1/x^2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you will get: \[\lim_{n \rightarrow \infty} {\ln (1+1/n) \over 1/n}=\lim_{n \rightarrow \infty} { {1/n^2 \over 1+1/n} \over 1/n^2}=\lim_{n \rightarrow \infty}{1 \over 1+1/n}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0which is equal to 1 as you can see.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so the top is 1 / 1 + 1/n and then you take the derivate of the inside of ln (1 + 1/n) right

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but this is the limit of the function after taking the ln, so the limit of your original function is e^1

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no problem.. just be a fan ;)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0AnwarA you still there I got another tought one its (1 + 1/sqrt(x))^x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0x is approaching what?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0use the same procedure we did with the first one.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok so I got to that part I got ( 1/2x ^ 3/2)/ 1 + 1/sqrt(x) / 1/x^2 but it doesnt look good to simplify to me

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you should use parentheses.
Ask your own question
Sign UpFind more explanations on OpenStudy
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.