For Exercises 11-16, identify the statements among a-h that follow directly from the given condition about x . a. csc x is undefined. b. sec x is undefined. c. The graph of y = sec x has a relative maximum at x . d. The graph of y = csc x has a relative minimum at x . e. The graph of y = sec x has a vertical asymptote. f. The graph of y = csc x has a vertical asymptote. g. The graph of y = csc x has a relative maximum at x . h. The graph of y = sec x has a relative minimum at x . sin x = 0
For Exercises 11-16, identify the statements among a-h that follow directly from the given condition about x . a. csc x is undefined. b. sec x is undefined. c. The graph of y = sec x has a relative maximum at x . d. The graph of y = csc x has a relative minimum at x . e. The graph of y = sec x has a vertical asymptote. f. The graph of y = csc x has a vertical asymptote. g. The graph of y = csc x has a relative maximum at x . h. The graph of y = sec x has a relative minimum at x . sin x = 0
Solution Summary: The author explains that the function y=mathrmcscx is an inverse of
For Exercises 11-16, identify the statements among
a-h
that follow directly from the given condition about
x
.
a.
csc
x
is undefined.
b.
sec
x
is undefined.
c. The graph of
y
=
sec
x
has a relative maximum at
x
.
d. The graph of
y
=
csc
x
has a relative minimum at
x
.
e. The graph of
y
=
sec
x
has a vertical asymptote.
f. The graph of
y
=
csc
x
has a vertical asymptote.
g. The graph of
y
=
csc
x
has a relative maximum at
x
.
h. The graph of
y
=
sec
x
has a relative minimum at
x
.
sin
x
=
0
Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .
1. Given the vector field F(x, y, z) = -zi, verify the relation
1
VF(0,0,0) lim
+0+ volume inside S
ff F• Nds
S.
where S, is the surface enclosing a cube centred at the origin and having edges of length 2€. Then,
determine if the origin is sink or source.
Let a = (-4, 5, 4) and 6 = (1,0, -1).
Find the angle between the vector
1) The exact angle is cos
2) The approximation in radians is
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