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 . The graph of y = cos x has a relative maximum at x .
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 . The graph of y = cos x has a relative maximum at x .
Solution Summary: The author explains that the trigonometric function y=mathrmsecx is an inverse of the function.
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
.
The graph of
y
=
cos
x
has a relative maximum at
x
.
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. A bicyclist is riding their bike along the Chicago Lakefront Trail. The velocity (in
feet per second) of the bicyclist is recorded below. Use (a) Simpson's Rule, and (b)
the Trapezoidal Rule to estimate the total distance the bicyclist traveled during the
8-second period.
t
0 2
4 6 8
V
10 15
12 10 16
2. Find the midpoint rule approximation for
(a) n = 4
+5
x²dx using n subintervals.
1° 2
(b) n = 8
36
32
28
36
32
28
24
24
20
20
16
16
12
8-
4
1
2
3
4
5
6
12
8
4
1
2
3
4
5
6
=
5 37
A 4 8 0.5
06
9
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
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