Use a graphing utility and the change-of-base properly to graph y = log 3 x , y = log 25 x , and y = log 100 x in the same viewing rectangle. a. Which graph is on the top in the interval (0,1)? Which is on the bottom? b. Which graph is on the lop in the interval (1, ∞ )? Which is on the bottom? c. Generalize by writing a statement about which graph is on top. which is on the bottom, and in which intervals, using y = log b x where b > 1. Disprove each statement in Exercises 116-120 by a. letting y equal a positive constant of your choice, and b. using a graphing utility to graph the function on each side of the equal sign. The two functions should have different graphs. showing that the equation is not true in general.
Use a graphing utility and the change-of-base properly to graph y = log 3 x , y = log 25 x , and y = log 100 x in the same viewing rectangle. a. Which graph is on the top in the interval (0,1)? Which is on the bottom? b. Which graph is on the lop in the interval (1, ∞ )? Which is on the bottom? c. Generalize by writing a statement about which graph is on top. which is on the bottom, and in which intervals, using y = log b x where b > 1. Disprove each statement in Exercises 116-120 by a. letting y equal a positive constant of your choice, and b. using a graphing utility to graph the function on each side of the equal sign. The two functions should have different graphs. showing that the equation is not true in general.
Solution Summary: The author explains the base-change property for logarithmic functions, which is mathematically expressed as mathrmlog_ba=
Use a graphing utility and the change-of-base properly to graph
y
=
log
3
x
,
y
=
log
25
x
, and
y
=
log
100
x
in the same viewing rectangle.
a. Which graph is on the top in the interval (0,1)? Which is on the bottom?
b. Which graph is on the lop in the interval (1,
∞
)? Which is on the bottom?
c. Generalize by writing a statement about which graph is on top. which is on the bottom, and in which intervals, using
y
=
log
b
x
where b > 1.
Disprove each statement in Exercises 116-120 by
a.letting y equal a positive constant of your choice, and
b.using a graphing utility to graph the function on each side of the equal sign. The two functions should have different graphs. showing that the equation is not true in general.
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 3 Solutions
Precalculus, Books A La Carte Edition Plus MyLab Math with eText -- Access Card Package (6th Edition)
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