The number N t of new cases of a flu outbreak for a given city is given by N t = 5000 ⋅ 2 − 0.04 t 2 , where t is the number of months since the outbreak began. a Find the average rate of change in the number of new flu cases between months 0 and 2, and interpret the result. Round to the nearest whole unit. b. Find the average rate of change in the number of new flu cases between months 4 and 6, and between months 10 and 12. c. Use a graphing utility to graph the function. Use the graph and the average rates of change found in parts (a) and (b) to discuss the pattern of the number of new flu cases.
The number N t of new cases of a flu outbreak for a given city is given by N t = 5000 ⋅ 2 − 0.04 t 2 , where t is the number of months since the outbreak began. a Find the average rate of change in the number of new flu cases between months 0 and 2, and interpret the result. Round to the nearest whole unit. b. Find the average rate of change in the number of new flu cases between months 4 and 6, and between months 10 and 12. c. Use a graphing utility to graph the function. Use the graph and the average rates of change found in parts (a) and (b) to discuss the pattern of the number of new flu cases.
The number
N
t
of new cases of a flu outbreak for a given city is given by
N
t
=
5000
⋅
2
−
0.04
t
2
,
where
t
is the number of months since the outbreak began.
a Find the average rate of change in the number of new flu cases between months 0 and 2, and interpret the result. Round to the nearest whole unit.
b. Find the average rate of change in the number of new flu cases between months 4 and 6, and between months 10 and 12.
c. Use a graphing utility to graph the function. Use the graph and the average rates of change found in parts (a) and (b) to discuss the pattern of the number of new flu cases.
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.
College Algebra with Modeling & Visualization (5th Edition)
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