Limits (infinity) (1 Viewer)

[aussiechica]

how do you solve limits as they approach infinity?
Ive tried 2 diff texts and neither of them are helpful

So any help here is appreciated Thanks!

 

[sukiyaki]

what i always do is plug in a huge number and if its negative i plug in a smallish number

and then you seen what it kinda is close to
lets say
as x--> infinity in "7 / x + 2"
7 / (very big number)

it almost equal to zero but it 0+ (tiny bit bigger then zero)

 

[wogboy]

Also when you need to sub in x=infinity into the expression to calculate the limit, always make sure that x is only in the denominator:

e.g. find lim (x->infinity) (x^2 - 2x + 2)/(3x^2 - x + 1)

{simply divide top & bottom of that fraction by x^2}
= lim (x->infinity) (1 - 2/x +2/x^2)/(3 - 1/x +1/x^2)

As a rule, anything divided by infinity (except infinity itself) is equal to zero. Also note that infinity = infinity^2 = infinity^1000 (infinity to the power of any positive number)

= (1 - 2/infinity + 2/infinity^2)/(3 - 1/infinity + 1/infinity^2)
= 1/3

If the function of x grows indefinitely (i.e. you can't put x into the denominator) then just say that "the limit doesn't exist"

e.g. lim (x->infinity) x^2
You can't simply put this into the form of a number divided by x like the previous question, so the limit doesn't exist.

 

[Winston]

ok all u need to know is that


the first thing u do is

look for the highest power



example question



x^4 - 1
----------

x^2 - x


x -> infinity



so in this case the highest power is x^4


you divide the whole numerator and denominator by x^4


so

x^4 1
----- - -------
x^4 x^4

------------------


x^2 x
------ - -------
x^4 x^4



= 1 - 1/ x^4
--------------
1/x^2 - 1/x^3


so as x -> infinity

then the answer is


= 1


u just eliminate all th ones with the x's in them


so yeah simple enough

 

[-=«MÄLÅÇhïtÊ»=-]

yeah
juz divide top and bottom by highest power

 

[Dangar]

ok i can follow wogboy's example, but i get stuck on yours Winston when you get to

1 - 1/ x^4
-------------
1/ x^2 - 1/ x^3


so then you say just cancel everything divided by x because it will equal zero. But then wouldn't you be left with 1 / 0 which you just can't do?

 

[...]

so for any expression that is fraction like, u divide it by the highest power???

 

[wogboy]

But then wouldn't you be left with 1 / 0 which you just can't do?

If you get an answer of 1/0 (or infinity) it means the limit does not exist, and this is what you write as your answer. This means the answer to Winston's limit is that "the limit doesn't exist".

If on the other hand you get an answer of 0/0 (or infinity/infinity) it means you haven't simplified the limit properly yet (i.e. you haven't put x in the denominator only). Try again.

so remember this:

1/0 (or infinity, or any non-zero number divided by zero) = The limit doesn't exist, but you've still done it properly.

0/0 (or infinity/infinity) = You've done a mistake, or haven't completely done the question. Try again.

Any other result (e.g. 1/2) = This is the answer, you've done it properly.

 

[...]

but Winston's answer is 1...

i got... 1/0 ....eekk!

 

[Winston]

sorry my bad lol it wasnt much of a good example i made up
if u guys give me one out of ur textbook i can explain it through easily

 

[...]

but is the answer 1?? or undefine