Year 12s: what will be the first way you research your future options? >>

Mathematics Question

ersdfrtg

Compute: Lim(x tends to infinity) x^3-x+2/-2x^3+x^2-1 ?

Reply 1

RDKGames

Study Forum Helper

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.

Reply 2

ersdfrtg

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 :/

Reply 3

Notnek

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

Reply 4

ersdfrtg

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
?

Reply 5

Notnek

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.

Reply 6

mik1a

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

Do they not teach brackets anymore?

Reply 7

RDKGames

Study Forum Helper

Original post by mik1a

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

No it doesn't.

Reply 8

mik1a

Original post by RDKGames

No it doesn't.

It does if you interpret brackets correctly. The x^3 is the dominant term.

Reply 9

RDKGames

Study Forum Helper

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.

Reply 10

mik1a

Yes, hence "do they not teach brackets anymore?"

Quick Reply

Related discussions

Latest

Articles for you

How to revise for A-level Maths exams: AQA explains what to do

How to revise for A-level Environmental Science exams: AQA explains what to do

How to revise for A-level Biology exams: AQA explains what to do

Students react after GCSE Maths Paper 1 on 19 May 2023

Mathematics Question

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you