when two fractions refer to the same whole and have the same denominators explain why you can compare only the numerators
1 answer:
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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
Answer:
or ≈6.59
Step-by-step explanation:
We can first begin by simplifying each of the numbers with exponents. Recall that in a fraction exponent, the numerator is the power, while the denominator is the root.
Take for example. The '2' in the fraction means we must take the square of 25. √25 = 5.
The '3' in the fraction means we take the power, which means we must cube '5'.
5³ = 125. Therefore, = 125. Use this process for the other numbers:
The new fraction would look like:
Which simplifies to:
or ≈6.59