Zero average value Find the value of a > 0 such that the average value of the following functions over R = { ( x , y ) : 0 ≤ x ≤ a , 0 ≤ y ≤ a } is zero. 53. f ( x , y ) = 4 − x 2 − y 2
Zero average value Find the value of a > 0 such that the average value of the following functions over R = { ( x , y ) : 0 ≤ x ≤ a , 0 ≤ y ≤ a } is zero. 53. f ( x , y ) = 4 − x 2 − y 2
Solution Summary: The author explains that the value of a is sqrt6. The integrable function satisfies the given condition.
Zero average valueFind the value of a > 0 such that the average value of the following functions over
R
=
{
(
x
,
y
)
:
0
≤
x
≤
a
,
0
≤
y
≤
a
}
is zero.
Find all numbers b such that the average value of f(x) = 7 + 8x - 6x2 on the interval [0, b] is equal to 8. (Enter your answers as a comma-separated list.)
1
b = (b-1)²- 2
X
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1
Please try again. Recall that the average value of a function f on an interval [a, b] is f
7f³f
f(x)dx.
b - a
ave
To find values b such that the average value of f on [0, b] is k, set up a function for fave with respect to b, and solve the equation f(b) = k for b.
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=
0.5x10 (0.0005)
since the absolute error made in variables x, y, z is
absolute values of the function f(x, y, z) = X ² at the point (2,3,4) and
Find the relative error
Find the average value of f(x) = 9x³ – 9x for the interval [8,12]
Note: Write the exact answer not the decimal approximation (for example write
not 0.8).
Answer: Average value is
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Definite Integral Calculus Examples, Integration - Basic Introduction, Practice Problems; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=rCWOdfQ3cwQ;License: Standard YouTube License, CC-BY