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mortonsalt

  • one year ago

Hello! I was wondering if someone can take a look at this question? (I'll post it below.)

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  1. mortonsalt
    • one year ago
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    The following limit represents the derivative of some function f at some number a. \[\lim_{h \rightarrow 0}\frac{(1+h)^{10} -1}{h}\] State f and a.

  2. zepdrix
    • one year ago
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    We have the limit definition of a derivative:\[\large\rm f'(a)=\lim\limits_{h\to0}\frac{f(a+h)-f(a)}{h}\] If you match up the pieces with the formula:\[\large\rm f(a+h)=(1+h)^{10},\qquad\qquad f(a)=1\]

  3. zepdrix
    • one year ago
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    So ummm

  4. zepdrix
    • one year ago
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    \[\large\rm f(\color{orangered}{a+h})=(\color{orangered}{1+h})^{10},\qquad\qquad f(a)=1\]If you look at this orange part here, you might be able to figure out what your a value is.

  5. zepdrix
    • one year ago
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    \[\large\rm f(\color{orangered}{a+h})=(\color{orangered}{1+h})^{10}\]And then if you choose to evaluate this at x, instead of a+h,\[\large\rm f(\color{orangered}{x})=(\color{orangered}{x})^{10}\]you should be able to see what your function is. See if this matches up with f(a)=1 though.

  6. zepdrix
    • one year ago
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    Hopefully that helps :U Stay salty friend.

  7. mortonsalt
    • one year ago
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    Sorry this took forever for me to check again. Thank you so much for your help @zepdrix

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