For Exercises 111-114, use the graph of y = f x to answer the following. (See Example 10) a . Determine f − 2 . b . Determine f 3 . c . Find all x for which f x = − 1. d . Find all x for which f x = − 4. e . Determine the x -intercept s . f . Determine the y -intercept . g . Determine the domain of f . h . Determine the range of f
For Exercises 111-114, use the graph of y = f x to answer the following. (See Example 10) a . Determine f − 2 . b . Determine f 3 . c . Find all x for which f x = − 1. d . Find all x for which f x = − 4. e . Determine the x -intercept s . f . Determine the y -intercept . g . Determine the domain of f . h . Determine the range of f
Solution Summary: The author explains the function f in the graph to determine the values of the functions.
For Exercises 111-114, use the graph of
y
=
f
x
to answer the following. (See Example 10)
a
. Determine
f
−
2
.
b
. Determine
f
3
.
c
. Find all
x
for which
f
x
=
−
1.
d
. Find all
x
for which
f
x
=
−
4.
e
. Determine the
x
-intercept
s
.
f
. Determine the
y
-intercept
.
g
. Determine the domain of
f
.
h
. Determine the range of
f
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.
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