Crude Oil Prices The price per barrel of crude oil in the period 1980–2013, in constant 2014 dollars, can be approximated by P ( t ) = 0.27 ( t − 1980 ) 2 − 8.6 ( t − 1980 ) + 93 dollars ( 1980 ≤ t ≤ 2013 ) , where t is the year. 30 Find P ' ( t ) and P ' ( 2010 ) . What does the second answer tell you about the price of crude oil?
Crude Oil Prices The price per barrel of crude oil in the period 1980–2013, in constant 2014 dollars, can be approximated by P ( t ) = 0.27 ( t − 1980 ) 2 − 8.6 ( t − 1980 ) + 93 dollars ( 1980 ≤ t ≤ 2013 ) , where t is the year. 30 Find P ' ( t ) and P ' ( 2010 ) . What does the second answer tell you about the price of crude oil?
Solution Summary: The author calculates the value of P'(t), if it is given that the price per barrel of crude oil in 1980-2013 and in constant 2014 dollars is approximate
Crude Oil Prices The price per barrel of crude oil in the period 1980–2013, in constant 2014 dollars, can be approximated by
P
(
t
)
=
0.27
(
t
−
1980
)
2
−
8.6
(
t
−
1980
)
+
93
dollars
(
1980
≤
t
≤
2013
)
,
where t is the year.30 Find
P
'
(
t
)
and
P
'
(
2010
)
. What does the second answer tell you about the price of crude oil?
3.1 Limits
1. If lim f(x)=-6 and lim f(x)=5, then lim f(x). Explain your choice.
x+3°
x+3*
x+3
(a) Is 5
(c) Does not exist
(b) is 6
(d) is infinite
1 pts
Let F and G be vector fields such that ▼ × F(0, 0, 0) = (0.76, -9.78, 3.29), G(0, 0, 0) = (−3.99, 6.15, 2.94), and
G is irrotational. Then sin(5V (F × G)) at (0, 0, 0) is
Question 1
-0.246
0.072
-0.934
0.478
-0.914
-0.855
0.710
0.262
.
2. Answer the following questions.
(A) [50%] Given the vector field F(x, y, z) = (x²y, e", yz²), verify the differential identity
Vx (VF) V(V •F) - V²F
(B) [50%] Remark. You are confined to use the differential identities.
Let u and v be scalar fields, and F be a vector field given by
F = (Vu) x (Vv)
(i) Show that F is solenoidal (or incompressible).
(ii) Show that
G =
(uvv – vVu)
is a vector potential for F.
Chapter 11 Solutions
Finite Mathematics and Applied Calculus (MindTap Course List)
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