A community for students.
Here's the question you clicked on:
 0 viewing
El_Arrow
 one year ago
need help with limit problem
El_Arrow
 one year ago
need help with limit problem

This Question is Closed

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0okay so my question is why is it dividing by n?

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0i thought you divided by the value with the largest power

Melodious
 one year ago
Best ResponseYou've already chosen the best response.0guys pls help me out in my question

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Next you should be asking why is it dividing by the term with largest power

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Notice that "n" is indeed the largest power in the denominator, but clearly you're missing the key point, dividing by "n" is not really necessary here

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Look at the expression \[\dfrac{n^3}{n+8}\] what happens to this term as "n" becomes large ? which one grows faster, numerator or denominator ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2are you saying "n+8" grows faster than "n^3" ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2plugin n=10, 100 etc and see which one is growing faster

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0no i meant the numerator

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Okay what about the value of expression as "n" gets large ?

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0it goes to infinity right

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2dw:1436635975751:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2As you can see the function f(x) = x^3/(x+8) is increasing without any bound as x increases, so the corresponding sequence diverges

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2They are dividing top and bottom by "n" so that it becomes easy for you to see the same

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2\[a_n = \dfrac{n^3}{n+8} = \dfrac{n^2}{1+8/n}\] "plugin" \(n = \infty\), the expression becomes \[ \dfrac{\infty^2}{1+8/\infty} = \dfrac{\infty^2}{1+0} = \infty\]

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0i think i understand better now

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2In general : For any rational function, \(f(x) = \dfrac{P(x)}{Q(x)}\) , as \(x\to\infty\), we have \(f(x)\to\pm\infty\) if the degree of \(P(x)\) is greater than the degree of \(Q(x)\)
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.