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cwrw238

  • 2 years ago

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

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

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

  3. agentc0re
    • 2 years ago
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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 #?

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

  5. agentc0re
    • 2 years ago
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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 )

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

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

  8. agentc0re
    • 2 years ago
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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?

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

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

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

  12. agentc0re
    • 2 years ago
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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.

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

  14. agentc0re
    • 2 years ago
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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?

  15. cwrw238
    • 2 years ago
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    yea awesome is right

  16. cwrw238
    • 2 years ago
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    thanks

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

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

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

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

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

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

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