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Math Help - Find the limit by evaluating the derivative only

  1. #1
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    Find the limit by evaluating the derivative only

    What does the title mean? What is it asking for? The question so far has consisted of:

    Find a function f and a number, (c), such that: \lim \limits_{h \to 0}\frac{(2+h)^5-32}{h}

    I found out that the answer was 80 but had to refresh my knowledge on how to expand binomials easily. I found this link that helped tremendously with that component.

    Now it's asking "Find the above limit by evaluating the derivative only". However this is a limit section of the textbook, we haven't learned the chain rule yet. Only the definition of the derivative, but it's not limiting my use of using the chain rule in this question. So what is it exactly asking and how would you approach this question? I would imagine what it is asking is easy but half the battle in math is understanding what it is asking for.
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  2. #2
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    Re: Find the limit by evaluating the derivative only

    Quote Originally Posted by Maskawisewin View Post
    What does the title mean? What is it asking for? The question so far has consisted of:

    Find a function f and a number, (c), such that: \lim \limits_{h \to 0}\frac{(2+h)^5-32}{h}

    I found out that the answer was 80 but had to refresh my knowledge on how to expand binomials easily. I found this link that helped tremendously with that component.

    Now it's asking "Find the above limit by evaluating the derivative only". However this is a limit section of the textbook, we haven't learned the chain rule yet. Only the definition of the derivative, but it's not limiting my use of using the chain rule in this question. So what is it exactly asking and how would you approach this question? I would imagine what it is asking is easy but half the battle in math is understanding what it is asking for.
    What are you expecting this limit to equal?
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  3. #3
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    Re: Find the limit by evaluating the derivative only

    Do you recognise that the "difference quotient" defining the derivative of [tex]x^5[/itex] at x= 2? What is the derivative of x^5? What is its value at x= 2?
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    Re: Find the limit by evaluating the derivative only

    Okay it took me a bit but I see now all it's asking is "go backwards". If this is the function plugged into the definition of the derivative then work backwards. It came across as very cryptic at first. Thank you.
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