Join TSR now and get all your revision questions answeredSign up now

Mathematics Question Watch

    • Thread Starter
    Offline

    0
    ReputationRep:
    Compute: Lim(x tends to infinity) x^3-x+2/-2x^3+x^2-1 ?
    • Community Assistant
    • Welcome Squad
    Online

    3
    ReputationRep:
    (Original post by ersdfrtg)
    Compute: Lim(x tends to infinity) x^3-x+2/-2x^3+x^2-1 ?
    Assuming it is \displaystyle \lim_{x \rightarrow \infty}\frac{x^3-x+2}{-2x^3+x^2-1} then just divide top and bottom by the highest degree of x and observe what happens to each term with x tending to infinity before evaluating what happens with the overall fraction.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by RDKGames)
    Assuming it is \displaystyle \lim_{x \rightarrow \infty}\frac{x^3-x+2}{-2x^3+x^2-1} then just divide top and bottom by the highest degree of x and observe what happens to each term with x tending to infinity before evaluating what happens with the overall fraction.
    And how would you divide this function by the highest degree of x? I tried doing long division, but it didn't work for me :/
    • TSR Support Team
    • Study Helper
    Offline

    3
    ReputationRep:
    (Original post by ersdfrtg)
    And how would you divide this function by the highest degree of x? I tried doing long division, but it didn't work for me :/
    The highest degree of x in this expression is 3 so divide top and bottom of this fraction by x^3.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by notnek)
    The highest degree of x in this expression is 3 so divide top and bottom of this fraction by x^3.
    But then that will give me negative powers: 1-x^-2+2x^-3 / -2+x^-2-x^-3
    ?
    • TSR Support Team
    • Study Helper
    Offline

    3
    ReputationRep:
    (Original post by ersdfrtg)
    But then that will give me negative powers: 1-x^-2+2x^-3 / -2+x^-2-x^-3
    ?
    It should be x^-1 instead of x^-2 on the bottom but other than that it's correct. Then the fraction can be written as

    \displaystyle \frac{1-\frac{1}{x^2} + \frac{2}{x^3}}{-2+\frac{1}{x^2} - \frac{1}{x^3}}

    Go through each term in this fraction and think about what happens as x\rightarrow \infty

    e.g. As x\rightarrow \infty, \frac{1}{x^2} tends to 0.
    Offline

    3
    ReputationRep:
    x^3-x+2/-2x^3+x^2-1 ---> inf as x ---> inf

    Do they not teach brackets anymore?
    • Community Assistant
    • Welcome Squad
    Online

    3
    ReputationRep:
    (Original post by mik1a)
    x^3-x+2/-2x^3+x^2-1 ---> inf as x ---> inf

    No it doesn't.
    Offline

    3
    ReputationRep:
    (Original post by RDKGames)
    No it doesn't.
    It does if you interpret brackets correctly. The x^3 is the dominant term.
    • Community Assistant
    • Welcome Squad
    Online

    3
    ReputationRep:
    (Original post by mik1a)
    It does if you interpret brackets correctly. The x^3 is the dominant term.
    Are you interpreting it as \displaystyle \lim_{x\rightarrow \infty} (x^3-x+\frac{2}{-2x^3}+x^2-1)? In which case that would be correct, otherwise I do not know what brackets you're talking about.
    Offline

    3
    ReputationRep:
    Yes, hence "do they not teach brackets anymore?"
 
 
 
Poll
How are you feeling about Results Day?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Quick reply
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.