Calculus: Single And Multivariable
7th Edition
ISBN: 9781119444190
Author: Hughes-Hallett, Deborah; Mccallum, William G.; Gleason, Andrew M.; Connally, Eric; Kalaycioglu, Selin; Flath, Daniel E.; Lahme, Brigitte; Lomen, David O.; Lock, Patti Frazer; Lovelock, David; Morris, Jerry; Lozano, Guadalupe I.; Mumford, David; Quinney, D
Publisher: WILEY
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Vectors u = 6(cos 60°i + sin60°j), v = 4(cos 315°i + sin315°j), and w = −12(cos 330°i + sin330°j) are given. Use exact values when evaluating sine and cosine.Part A: Convert the vectors to component form and find −7(u • v). Show every step of your work.Part B: Convert the vectors to component form and use the dot product to determine if u and w are parallel, orthogonal, or neither. Justify your answer.
Suppose that one factory inputs its goods from two different plants, A and B, with different costs, 3 and 7
each respective. And suppose the price function in the market is decided as p(x, y) = 100 - x - y where
x and y are the demand functions and 0 < x, y. Then as
x =
y=
the factory can attain the maximum profit,
f(x) =
=
x - 3
x²-9
f(x) = {x +
1
x > 3
4
x < 3
-10
5
10
5
5.
10
5-
07.
10
-10
-5
0
10
5
-101
:: The function has a “step" or "jump" discontinuity at x = 3 where f(3) = 7.
:: The function has a value of f (3), a limit as x approaches 3, but is not continuous at x = 3.
:: The function has a limit as x approaches 3, but the function is not defined and is not continuous at x = 3.
:: The function has a removable discontinuity at x=3 and an infinite discontinuity at x= -3.
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