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iamMJae

  • one year ago

If it exists, what is:

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  1. iamMJae
    • one year ago
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    \[\lim_{h \rightarrow 0}\frac{ f(3+h)-f(3) }{ h }\]

  2. Zale101
    • one year ago
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    What is the function f ?

  3. iamMJae
    • one year ago
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    Function f? There should be a definition for f(x)?

  4. Zale101
    • one year ago
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    I'm sorry @iamMJae. You're question is not fully written. You need to have some function. If you want to go ahead and sub x=0, you'll get a 0 in the denominator which makes it undefined.

  5. iamMJae
    • one year ago
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    That's all we got. All the question says: If it exists, what is: \[\lim_{h \rightarrow 0}\frac{ f(3+h)-f(3) }{ h }\]

  6. nincompoop
    • one year ago
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    if what exists?

  7. iamMJae
    • one year ago
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    If I understand the question correctly, it's the limit. "If the limit exists..."

  8. nincompoop
    • one year ago
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    does it exist?

  9. freckles
    • one year ago
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    do you know the definition of the derivative (if it exist)

  10. nincompoop
    • one year ago
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    can a limit exist without a function?

  11. freckles
    • one year ago
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    well the question says what is the limit if it exists and if exists then we know another we know the value to be...

  12. freckles
    • one year ago
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    that is if \[\lim_{h \rightarrow 0}\frac{g(a+h)-g(a)}{h} \text{ exists } \\ \text{ we call this value } \frac{dg(x)}{dx}|_{x=a}\]

  13. freckles
    • one year ago
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    and that is all I can do without knowing what g actually is

  14. freckles
    • one year ago
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    or f in your case

  15. nincompoop
    • one year ago
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  16. anonymous
    • one year ago
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    It simply is \(f'(3)\)

  17. iamMJae
    • one year ago
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    @mukushla How did it become \[f'(3)\] ?

  18. freckles
    • one year ago
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    He used definition of derivative

  19. freckles
    • one year ago
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    This is what I gave you above except your f is my g and your 3 is my a

  20. iamMJae
    • one year ago
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    @freckles The derivative is supposed to be the limit? I'm now confused.

  21. freckles
    • one year ago
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    The derivative of g at a is the way I defined it above

  22. iamMJae
    • one year ago
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    But we're looking for the limit.

  23. freckles
    • one year ago
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    http://tutorial.math.lamar.edu/Classes/CalcI/DefnOfDerivative.aspx see the definition.. Though I already wrote it above

  24. anonymous
    • one year ago
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    @iamMJae you don't have the function, but question says "if the limit exists", this means if the limit exists the value of it will be \(f'(3)\), whatever \(f(x)\) might be.

  25. iamMJae
    • one year ago
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    I'm still quite confused but... We can conclude this problem with, "If it exists, the limit is \[f'(3)\]"?

  26. ZeHanz
    • one year ago
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    There should be a little more info here imo. We have to assume there is some function f, with some formula to calculate values of it. You then could calculate the given limit. If THAT exists, it is, by definition, the derivative of f in x=3, so yes, if this limit exists, it is \(f'(3)\)

  27. mathmate
    • one year ago
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    The question is a check for the understanding of the definition of derivatives. It gave the definition of the derivative and see if the students can recognize it, so there is nothing unclear about the question. @mukushla gave a direct answer.

  28. ZeHanz
    • one year ago
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    @mathmate: I'm sure the original question was clear, it's just that @iamMJae was a little terse in her question here.

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