Question 990327
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).
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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