anonymous
  • anonymous
how do you estimate the instantaneous rate of change
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
first i made of tables of points that are getting closer and closer the point but im not sure what to do next
anonymous
  • anonymous
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 \[\lim_{t \rightarrow 0}(f(t)/t)\]
anonymous
  • anonymous
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?

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myininaya
  • myininaya
\[f'(10) \text { \to find instaneous rate of change at x=10}\]
myininaya
  • myininaya
you have x and t going on there that is weird
anonymous
  • anonymous
oh ya the t's are supposed to be x's
TuringTest
  • TuringTest
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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