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# homework5 - Math 20C(Lecture C Homework 5(Due on December...

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Math 20C (Lecture C) - Homework 5 (Due on December 10th, Monday by 3pm) This homework covers sections 15.1-4 from Stewart’s book. You need to return only the questions marked with ( * ) . The others are provided for practicing purposes. 1.(*) (Section 15.1) Consider the functions f ( x, y ) = p 4 - x 2 - y 2 and g ( x, y ) = p x 2 + y 2 deﬁned over the domain D = { ( x, y ) : 0 x 1 , 0 y 1 } . a. Approximate the volumes under the functions over the domain D by using the midpoint sum and dividing the intervals [0 , 1] along the x and y axes into two subintervals of length 0.5 or equivalently dividing D into four rectangles with side-lengths Δ x = Δ y = 0 . 5. b. The left and right sum are the Riemann sums such that the function values are evaluated at the lower-left and upper-right end points of each rectangle. Without calculating the left and right sum order the left, midpoint and right sum with Δ x = Δ y = 0 . 5 from the smallest to the largest for the functions f ( x, y

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homework5 - Math 20C(Lecture C Homework 5(Due on December...

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