Answer the question.Consider a function f(x, y, z), where the independent variables are constrained to lie on the curve 
(t) = x(t)i + y(t)j + z(t)k. What mathematical fact forms the basis for the method of Lagrange multipliers?
A. ?f??g = 0
B. f approaches a local extremum as ? ? 0.
C. ?f?
= 0
D. ?g = 0
Answer: C
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Use the bar graph, which shows the receipts of the federal government (in billions of dollars) for selected years from 1996 through 2006. In this exercise you are given the expenditures of the federal government. Find the magnitude of the surplus or deficit for the year 2006.
(Source: U.S. Office of Management and Budget)
?
Year
Receipts
Expenditures
|Receipts - Expenditures|
?2006
?
?2655.4
?
?
A. ?
| Year | Receipts | Expenditures | |Receipts - Expenditures| |
| ?2006 | ?2407.3 | ?2655.4 | ?248.1 |
B. ?
| Year | Receipts | Expenditures | |Receipts - Expenditures| |
| ?2006 | ?2407.3 | ?2655.4 | ?102.4 |
C. ?
| Year | Receipts | Expenditures | |Receipts - Expenditures| |
| ?2006 | ?2407.3 | ?2655.4 | ?105.4 |
D. ?
| Year | Receipts | Expenditures | |Receipts - Expenditures| |
| ?2006 | ?2407.3 | ?2655.4 | ?107.4 |
E. ?
| Year | Receipts | Expenditures | |Receipts - Expenditures| |
| ?2006 | ?2407.3 | ?2655.4 | ?107 |
Graph the function.y = sin 
x 
A. 
B. 
C. 
D. 
Decide whether or not the functions are inverses of each other.f(x) = x3 - 5, g(x) =
A. Yes B. No
Give the equation of the oblique asymptote, if any, of the function.h(x) = 
A. y = 
B. y = x + 
C. y = 
x
D. no oblique asymptote