tutorial6

tutorial6 - will best fit the data. (You are not required...

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MATH1211/10-11(2)/Tu6/TNK THE UNIVERSITY OF HONG KONG DEPARTMENT OF MATHEMATICS MATH1211 Multivariable Calculus 2010-11 2nd Semester: Tutorial 6 Date of tutorial classes: March 17–18. (The section/problem numbers in the following refer to those in the textbook.) 1. Suppose ( x 1 ,y 1 ) ,..., ( x n ,y n ) are some data you obtained, and you want to find an equation of the form y = ax 2 + bx + c (where a,b,c are some constants) to predict the values of y from known values of x . (a) Use the method of least squares to construct a function D ( a,b,c ) that gives the sum of the squares of the distances between the observed and predicted y -values of the data. (b) Find a system of equations that will give the values of a,b,c such that the corresponding curve
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Unformatted text preview: will best fit the data. (You are not required to solve for the values of a,b,c .) 2. ( § 5.1 no.8) Find the volume of the region bounded on top by the plane z = x + 3 y + 1, on the bottom by the xy-plane, and on the sides by the planes x = 0 , x = 3 , y = 1 , y = 2. 3. ( § 5.1 no.16) Suppose that f is a nonnegative-valued, continuous function defined on R = { ( x,y ) | a ≤ x ≤ b, c ≤ y ≤ d } . If f ( x,y ) ≤ M for some positive number M , explain why the volume V under the graph of f over R is at most M ( b-a )( d-c ). 4. ( § 5.2 no.12) Integrate the function f ( x,y ) = 3 xy over the region bounded by y = 32 x 3 and y = √ x . 1...
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This note was uploaded on 05/04/2011 for the course MATH 1211 taught by Professor Wang during the Spring '11 term at HKU.

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