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grantmasini

  • 2 years ago

Limits

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  1. grantmasini
    • 2 years ago
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    \[\cos x \lim_{h \rightarrow 0}\frac{ \sin h }{ h }\]

  2. zzr0ck3r
    • 2 years ago
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    have you learned lhospital rule ?

  3. grantmasini
    • 2 years ago
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    no.

  4. zzr0ck3r
    • 2 years ago
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    what are you doing in class?

  5. zzr0ck3r
    • 2 years ago
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    squeeze theorem?

  6. grantmasini
    • 2 years ago
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    this is one of the last steps in a limit problem from the first unit (limits). it's supposed to evaluate to cosx*1=cosx. I don't understand how sinh/h comes out to be 1?

  7. zzr0ck3r
    • 2 years ago
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    well, there is a thing called La'Hospital rule, that says when you run a limit and get 0/0 you can take the derivative of the top and the derivative of the bottom and then run the limit again so your limit lim of sin(h)/h = lim of cos(h)/1 = lim cos(h) and at 0 that is 1

  8. zzr0ck3r
    • 2 years ago
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    l'hopital's rule

  9. grantmasini
    • 2 years ago
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    lol, we are on the first unit. haven't learned derivates, or any of the theorems or rules.

  10. grantmasini
    • 2 years ago
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    can someone just explain how the limit of sinh/h is 1?

  11. grantmasini
    • 2 years ago
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    derivatives*

  12. zzr0ck3r
    • 2 years ago
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    hmm

  13. zzr0ck3r
    • 2 years ago
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    do you know the squeeze theorem?

  14. zzr0ck3r
    • 2 years ago
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    There is a geometric proof http://www.youtube.com/watch?v=Ve99biD1KtA I don't know of an elementary way of showing this limit without geometry and quite a bit of explaining...watch that video.

  15. grantmasini
    • 2 years ago
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    all right, thanks

  16. zzr0ck3r
    • 2 years ago
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    np

  17. PROSS
    • 2 years ago
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    It appears that you are beginning the study of Calculus with the topic of limits. We often will use a table of values as they approach the limit from the left and from the right. This is the first method you may want to use. A second method that is used is to look at the graph of the function. You can easily see that the limit as h approaches 0 from the left and right is 1. I hope this helps.

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