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mathcalculus

  • 2 years ago

HELP: Use your knowledge of the derivative to compute the limit given below: The derivative that is being calculated is

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  1. mathcalculus
    • 2 years ago
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  2. mathcalculus
    • 2 years ago
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    im confused. am i suppose to use the power rule or quotient rule to find the derivative?

  3. asnaseer
    • 2 years ago
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    do you know how to write the general form for the derivative of f(x)?

  4. SithsAndGiggles
    • 2 years ago
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    It sounds like the problem is asking you to recognize that the given limit is the definition of the derivative of some function. Given \(\displaystyle\lim_{h\to0}\dfrac{f(x+h)-f(x)}{h}\), find \(f(x)\). Then, simply compute the derivative.

  5. asnaseer
    • 2 years ago
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    ^

  6. mathcalculus
    • 2 years ago
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    yes

  7. mathcalculus
    • 2 years ago
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    im not sure how to start this

  8. SithsAndGiggles
    • 2 years ago
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    Well do you know how to find the derivative? The way the question is stated makes it sound like you've learned some of or all the "rules" for differentiation. In this case, since \(f(x)=\dfrac{1}{x^6}\), you would apply the power rule to find the derivative, and that would be your answer.

  9. mathcalculus
    • 2 years ago
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    right i used the power rule.

  10. SithsAndGiggles
    • 2 years ago
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    Okay, so that gives you \[f(x)=\frac{1}{x^6}=x^{-6}~\Rightarrow~f'(x)=\cdots\]

  11. mathcalculus
    • 2 years ago
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    -6/x^7

  12. SithsAndGiggles
    • 2 years ago
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    Right.

  13. mathcalculus
    • 2 years ago
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    ^_^

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