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anonymous

  • 4 years ago

how do you estimate the instantaneous rate of change

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  1. anonymous
    • 4 years ago
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    first i made of tables of points that are getting closer and closer the point but im not sure what to do next

  2. anonymous
    • 4 years ago
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    if you are evaluating "instantaneous" rate of change, you'll evaluate your function as t (time) goes to zero, i think u need to use limits \[\lim_{t \rightarrow 0}(f(t)/t)\]

  3. anonymous
    • 4 years ago
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    so my equation is f(x)=(100x^2)/(t^(3)+5t^(2)-100x+380) and in want to know the instantaneous velocity at f(10) i would take the limit of that equation as x->10?

  4. myininaya
    • 4 years ago
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    \[f'(10) \text { \to find instaneous rate of change at x=10}\]

  5. myininaya
    • 4 years ago
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    you have x and t going on there that is weird

  6. anonymous
    • 4 years ago
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    oh ya the t's are supposed to be x's

  7. TuringTest
    • 4 years ago
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    Instantaneous rate for change is\[f'(x)=\lim_{\Delta x \rightarrow 0}{f(x+\Delta x)-f(x)\over\Delta x}\]so the estimation is the same formula with a finite sized Delta x; i.e. no limit\[f'(x)=\lim_{\Delta x \rightarrow 0}{f(x+\Delta x)-f(x)\over\Delta x}\approx{f(x+\Delta x)-f(x)\over\Delta x}\]for reasonably small Delta x. How small Delta x has to be for a good estimate depends of how curved the function is around the point in question.

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