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 .
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?
2. Find a matrix A with the following qualities
a. A is 3 x 3.
b. The matrix A is not lower triangular and is not upper triangular.
c. At least one value in each row is not a 1, 2,-1, -2, or 0
d. A is invertible.
Find the exact area inside r=2sin(2\theta ) and outside r=\sqrt(3)
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