Original price of a sofa: $620.00 Discount: 25%, Selling Price?
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Answer:
where x₁ and x₂ are values in the interval [x,y] respectively
Step-by-step explanation:
Well, first to determine the average rate of change of a function, you should have the interval of the values of x for the function.
So lets assume you have a function;
And the interval as [1,3]
Then the average rate of change for the function f(x) will be;
where x₁ and x₂ are the interval coordinates x,y respectively. In this case x₁=1 and x₂=3
To find the average rate of change in this example will be;
Answer:
a) integral = 24.72
b) |Error| ≤ 0.4267
Step-by-step explanation:
a)
The integral:
can be approximated with the midpoint rule, as follows:
6.7*(0.8 - 0.0) + 8.9*(1.6 - 0.8) + 6.9*(2.4-1.6) + 8.4*(3.2 - 2.4) = 24.72
(that is, all the intervals are 0.8 units length and f(x) is evaluated in the midpoint of the interval)
b)The error bound for the midpoint rule with <em>n</em> points is:
|Error| ≤ K*(b - a)^3/(24*n^2)
where <em>b</em> and are the limits of integration of the integral and K = max |f''(x)|
Given that -5 ≤ f''(x) ≤ 1, then K = 5. Replacing into the equation:
|Error| ≤ 5*(3.2 - 0)^3/(24*4^2) = 0.4267