The average value or mean value of a continuous function f x , y R = a , b × c , d is defined as f ave = 1 A R ∬ R f x , y d A Where A R = b − a d − c is the area of the rectangle R (compare to Definition 5.8.1). Use this definition in these exercises. Find the average value of f x , y = y sin x y over the rectangle 0 , 1 × 0 , π / 2 .
The average value or mean value of a continuous function f x , y R = a , b × c , d is defined as f ave = 1 A R ∬ R f x , y d A Where A R = b − a d − c is the area of the rectangle R (compare to Definition 5.8.1). Use this definition in these exercises. Find the average value of f x , y = y sin x y over the rectangle 0 , 1 × 0 , π / 2 .
2. For F = (xz³,2y*x², 5z?y) find:
a. div F
b. Curl F
c. and find div(curl F)
Consider the function frx)=Cax+7x=
PartA: IS fcx) continuous at X= -2?
Justify answer.
x+x+1 K7-2
Part B: ExPlain why fCX), is continuous at a ll
0ther Points cwhen x7-2).
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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