Question

I continue to have trouble solving limits in calculus. Can anybody recommend a good website which deals with this. An 'idiots guide' ?

Answer 1

1) People who are not idiots don't need an idiots' guide.
2) http://tutorial.math.lamar.edu/

Answer 2

lol - thank you parthkohli - i'll take a look

Answer 3

You're not an idiot. Limits are tricky business. What kind of limits are you having trouble with? Limits approaching infinity? Zero? or some other finite #?

Answer 4

i think limits approaching 0 and infinity

Answer 5

Limits approaching infinity have 3 "rules" to make this a bit more simple.
\[\lim_{x \rightarrow \infty} {x^4+123x^3-x^2-238x+10^6 \over 34x^4-38x+11}\]
\[\lim_{x \rightarrow \infty} {x^4+123x^3-x^2-238x+10^6 \over 34x^5-38x+11}\]
\[\lim_{x \rightarrow \infty} {x^7+123x^3-x^2-238x+10^6 \over 34x^4-38x+11}\]

Lets just talk about what we see going on here.
Can you tell me what you notice in the first example? (besides that it looks like a mess :D )

Answer 6

well - the degree of top and bottom poly's are the same

Answer 7

sorry i didn't answer earlier - i was called away

Answer 8

It's no problem. And you're correct. The degree of the polynomials are the same on top and bottom. So lets let this rule be our first.
If the highest degree polynomials are the same in the denominator as in the numerator, then the limit as it approaches infinity will ALWAYS be the ration of the coefficients. In this case that ratio is \[1\over34\]

The reason why this is is if you multiplied the entire equation by \[{1 \over x^4}\over{1 \over x^4 }\]
We would then have a lot of cases were there would be some number divided by some form of x. \[1 \over x\] for x= infinity will always go to zero.
So on top you would just have 1 + 0 - 0 - 0 + 0
and on bottom you would have 34 - 0 +0

Does that help with the first example? Any questions?

Answer 9

thanks - no questions - thats very clear

Answer 10

Awesome!!! Lets go to example two. What do you notice there?

Answer 11

the denominator has higher degree

Answer 12

Right. Do you have a guess as to what might happen?? ... shoot i have to go and i don't want to leave you hanging. A good video about this is: http://patrickjmt.com/limits-at-infinity-basic-idea-and-shortcuts-for-rational-functions/

WHen i get back i can help further explain what's going on if the video doesn't help.

Answer 13

do we multiply top and bottom by 1 /x^5 ?

Answer 14

For the second example, multiple the top and bottom in the same way we did the first one but do it by the highest degree polynomial. You see that you get 0/(some number). therefor these types of limits when approaching infinity ALWAYS go to zero! how awesome is that?

Answer 15

yea awesome is right

Answer 16

thanks

Answer 17

ill take a look at the video

Answer 18

I'm back! :D did you have questions still about limits approaching infinity?

Answer 19

no - i'm checking out the video which is very good.
thanks very much for your help

Answer 20

Also, not to forget mentioning http://khanacademy.com

Answer 21

@parthkohi oh right - thanks

Answer 22

You're welcome.
Can you please give the medal to @agentc0re? He deserves it all. (: