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mathcalculus

  • 2 years ago

HELP: use your knowledge of the derivative to compute the limit given below: lim (x+h)^(-3.25) -x^(-3.25)/h h->0 the derivative that is being calculated is dy/dx

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  1. BangkokGarrett
    • 2 years ago
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    That is just a complicated way of asking you: "What is the derivative of x^-3.25 ?"

  2. mathcalculus
    • 2 years ago
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    oh.. but how do i get to my answer? what are the steps and why is it questioned in this format?

  3. mathcalculus
    • 2 years ago
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    i know how to find the derivative ^

  4. mathcalculus
    • 2 years ago
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    -3.25x^-4.25

  5. mathcalculus
    • 2 years ago
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    do we use quotient rule?

  6. BangkokGarrett
    • 2 years ago
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    If you are allowed to "use your knowledge of the derivative", you could say that by definition the derivative of a function (here your function is x^-3.25) is the limit as h approaches 0 of f(x + h) - f(x). Therefore, this limit equals the derivative of x^-3.25 which is (and you know how to do the derivative, right?)

  7. BangkokGarrett
    • 2 years ago
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    yes your derivative is correct

  8. BangkokGarrett
    • 2 years ago
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    no quotient rule here

  9. mathcalculus
    • 2 years ago
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    so whats the main purpose of these kinds of questions? for ex: what if it was a square root problem... do we find only the deriative of the f(x+h) an thats our answer?

  10. BangkokGarrett
    • 2 years ago
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    find the derivative of f(x)...forget about the h. I think your prof just want's you to see how easy it is to do limits in that form now that you can do derivatives. Or maybe he / she wants to reinforce how derivatives relate to limits.

  11. mathcalculus
    • 2 years ago
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    ex: (x+h)^(12/12) -x^(12/12) / h

  12. mathcalculus
    • 2 years ago
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    so do we find the derivative: 12?

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