SOLUTION: Determine the average rate of change of the function between the given values of the variable. g(x)= 5/x+9 x=0, x=h I really need help :/

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Question 990327: Determine the average rate of change of the function between the given values of the variable.
g(x)= 5/x+9
x=0, x=h
I really need help :/
Found 2 solutions by stanbon, Boreal:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Determine the average rate of change of the function between the given values of the variable.
g(x)= 5/x+9
x=0, x=h
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Note: Average rate = (change in y)/(change in x)
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Ans: Ave rate = [g(h)-g(0)]/(h-0)
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= [5/(h+9)-(5/9)]/h
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= (5/h)[9-(h+9)]/[9*(h+9)]
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= -5/[9(h+9)]
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Cheers,
Stan H.
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Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
g(x)=5/(x+9)
that is between (5/9) and (5/h+9)
subtract the first from the second and divide by h.
(5/h+9)-(5/9)={1/9(h+9)}*-5(h+9)+45;
the numerator is -5h-45+45=-5h
the denominator is 9(h+9)
The difference is -(5/9) (h/h+9);
I still have to divide by h to get the average over the interval 0 to h.
That is -5/9(h+9).
===
with calculus, the first derivative is -5/(x+9)^2
evaluated at 0, it is -5/81
evaluated at h, it is -5/9(h+9), and as h goes to 0, the result is-5/81