James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

phy of Simpson on page 520.) The example that he gave to illustrate the method was to
solve the system of equations
x x 1 y y − 1000 x y 1 y x − 100
In other words, he found the points of intersection of the curves in the figure. Use the
method of part (a) to find the coordinates of the points of intersection correct to six
decimal places.
y
4
x x +y y =1000
2
x y +y x=100
FIGURE FOR PROBLEM 6
0
2 4 x
7et14ppx06
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MasterID: 01651
7. If the ellipse x 2 ya 2 1 y 2 yb 2 − 1 is to enclose the circle x 2 1 y 2 − 2y, what values of a
and b minimize the area of the ellipse?
8. Show that the maximum value of the function
f sx, yd −
sax 1 by 1 cd2
x 2 1 y 2 1 1
is a 2 1 b 2 1 c 2 .
Hint: One method for attacking this problem is to use the Cauchy-Schwarz Inequality:
(See Exercise 12.3.61.)
| a ? b | < | a | | b |
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