## cwrw238 3 years ago I continue to have trouble solving limits in calculus. Can anybody recommend a good website which deals with this. An 'idiots guide' ?

1. ParthKohli

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

2. cwrw238

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

3. agentc0re

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 #?

4. cwrw238

i think limits approaching 0 and infinity

5. agentc0re

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 )

6. cwrw238

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

7. cwrw238

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

8. agentc0re

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?

9. cwrw238

thanks - no questions - thats very clear

10. agentc0re

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

11. cwrw238

the denominator has higher degree

12. agentc0re

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.

13. cwrw238

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

14. agentc0re

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?

15. cwrw238

yea awesome is right

16. cwrw238

thanks

17. cwrw238

ill take a look at the video

18. agentc0re

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

19. cwrw238

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

20. ParthKohli

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

21. cwrw238

@parthkohi oh right - thanks

22. ParthKohli

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