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Calculate the average rate of change of the given function f over the intervals [a, a + h] where h = 1, 0.1, 0.01, 0.001, and 0.0001. (Technology is recommended for the cases h = 0.01, 0.001, and 0.0001.) HINT [See Example 4.] (Round your answers to five decimal places.) f(x) = 3 x ; a = 7

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Step-by-step explanation:

average rate of change of function is given by :

[tex]f= (f(a+h)-f(a))/h[/tex]

where

[tex]f(x)=3x[/tex]

and a= 7

so inserting values is formula for h=1

[tex]f=(f(7+1)-f(7))/1[/tex]

[tex]f= f(8)-f(7)= 3(8)-3(7)=24-21=3[/tex]

now for h= 0.1

[tex]f=(f(7+0.1)-f(7))/0.1=(f(7.1)-f(7))/0.1=(3(7.1)-3(7))/0.1[/tex]

[tex]f=3[/tex]

similarly average rate of change of given function is same for all given step sizes.

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