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cwrw238 Group Title

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

  • 2 years ago
  • 2 years ago

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

    • 2 years ago
  2. cwrw238 Group Title
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    lol - thank you parthkohli - i'll take a look

    • 2 years ago
  3. agentc0re Group Title
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    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 #?

    • 2 years ago
  4. cwrw238 Group Title
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    i think limits approaching 0 and infinity

    • 2 years ago
  5. agentc0re Group Title
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    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 )

    • 2 years ago
  6. cwrw238 Group Title
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    well - the degree of top and bottom poly's are the same

    • 2 years ago
  7. cwrw238 Group Title
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    sorry i didn't answer earlier - i was called away

    • 2 years ago
  8. agentc0re Group Title
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    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?

    • 2 years ago
  9. cwrw238 Group Title
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    thanks - no questions - thats very clear

    • 2 years ago
  10. agentc0re Group Title
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    Awesome!!! Lets go to example two. What do you notice there?

    • 2 years ago
  11. cwrw238 Group Title
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    the denominator has higher degree

    • 2 years ago
  12. agentc0re Group Title
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    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.

    • 2 years ago
  13. cwrw238 Group Title
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    do we multiply top and bottom by 1 /x^5 ?

    • 2 years ago
  14. agentc0re Group Title
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    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?

    • 2 years ago
  15. cwrw238 Group Title
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    yea awesome is right

    • 2 years ago
  16. cwrw238 Group Title
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    thanks

    • 2 years ago
  17. cwrw238 Group Title
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    ill take a look at the video

    • 2 years ago
  18. agentc0re Group Title
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    I'm back! :D did you have questions still about limits approaching infinity?

    • 2 years ago
  19. cwrw238 Group Title
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    no - i'm checking out the video which is very good. thanks very much for your help

    • 2 years ago
  20. ParthKohli Group Title
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    Also, not to forget mentioning http://khanacademy.com

    • 2 years ago
  21. cwrw238 Group Title
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    @parthkohi oh right - thanks

    • 2 years ago
  22. ParthKohli Group Title
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    You're welcome. Can you please give the medal to @agentc0re? He deserves it all. (:

    • 2 years ago
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