Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 11, Problem 45SP
To determine
To calculate: the largest and the smallest value of the function “f” on the specified closed bounded set “S”
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Suppose that X and Y are independent measurement of a quantity μ.
E(X) = E(Y) = μ, σX ≠ σY, Z = αX + (1 - α)Y, α ∈ [0, 1]
(a) Show that E(X) = μ.
(b) Find α in terms of σX and σY to minimize V(Z).
(c) Under what circumstance is it better to use the average (X+Y)/2 than either X or Y alone?
4) Find the critical points of the function f(x, y) =exp((−x3/3)+x−y2 ) and determine their type.
b) Find the global extrema of the function of part a) on the domain D={(x, y)|−2≤x≤2,−2≤y≤2}.
Find the Green's function of the boundary value problem
y"= f(x)
y(0) = 0, y(1) = 0
Chapter 11 Solutions
Calculus
Ch. 11.1 - Prob. 1PSCh. 11.1 - Prob. 2PSCh. 11.1 - Prob. 3PSCh. 11.1 - Prob. 4PSCh. 11.1 - Prob. 5PSCh. 11.1 - Prob. 6PSCh. 11.1 - Prob. 7PSCh. 11.1 - Prob. 8PSCh. 11.1 - Prob. 9PSCh. 11.1 - Prob. 10PS
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- At noon, ship A is 45 miles south of Ship B. Ship A is sailing north at a rate of 15 miles per hour. Ship B is sailing west at a rate of 15 miles per hour. When is the distance between the two ships minimized? In the field below enter the time at which the distance between the ships is minimal.arrow_forwardProblem 11 The volume of the solid obtained by rotating the region enclosed by y=(x^2), y=6x, about the line x=0 can be computed using the method of disks or washers via an integral V=∫[upper limit=b, lower limit=a]________dy with limits of integration a=_______ and b=________arrow_forwardProblem 9 The volume of the solid obtained by rotating the region bounded by x=(9y^2), y=1, x=0 about the y-axis can be computed using the method of washers or disks via an integral V=∫________________dy (with lower limit of a and upper limit of b) with limits of integration a=_________ and b=_________ The volume of this solid can also be computed using cylindrical shells via an integral V=∫_______________dx (with lower limt of alpha and upper limit of beta) with limits of integration alpha=_________ and beta=__________ In either case, the volume is V=______________ cubic unitsarrow_forward
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