Use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integral for convergence. If more. than one method applies, use whatever method you prefer. 00 S Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. 1 O B. dx x +6 The comparison function g(x)= can be used with a comparison test to determine convergence, but since 3 OA. 00 S 0 √x +6 √√x +6 this choice of g(x) is discontinuous at x = OF dx 00 S dx √√x +6 and g(x) are both continuous and positive over the interval. f(x) > g(x) over this interval, and the integral of g(x) over this interval diverges. (Type your answer in interval notation.) 1 this choice of g(x) is discontinuous at x = dx √x+6 dx 1 The comparison function g(x)= can be used with a comparison test to determine convergence, but since 00 OD S dx √√x +6 -S. interval converges, and J dx √√x+6 (Type your answer in interval notation.) dx S OC. The integral converges because 1 ndj- dx √x +6 S and g(x) are both continuous and positive over the interval 0 g(x) over this interval, the integral of g(x) 1 dx D must be rewritten as has the exact value dx By the Direct Comparison Test, the integral converges because f(x) must be rewritten as 1 The comparison function g(x)= can be used with a comparison test to determine convergence, but since x² Ĵ is not defined. must be rewritten as has a finite value. dx D x+6 must be rewritten as dx . By the Limit Comparison Test, the integral diverges because f(x) +6 f(x) and g(x) are both continuous and positive over the interval .0< lim X-9(x) 00, and the integral of g(x) over
Use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integral for convergence. If more. than one method applies, use whatever method you prefer. 00 S Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. 1 O B. dx x +6 The comparison function g(x)= can be used with a comparison test to determine convergence, but since 3 OA. 00 S 0 √x +6 √√x +6 this choice of g(x) is discontinuous at x = OF dx 00 S dx √√x +6 and g(x) are both continuous and positive over the interval. f(x) > g(x) over this interval, and the integral of g(x) over this interval diverges. (Type your answer in interval notation.) 1 this choice of g(x) is discontinuous at x = dx √x+6 dx 1 The comparison function g(x)= can be used with a comparison test to determine convergence, but since 00 OD S dx √√x +6 -S. interval converges, and J dx √√x+6 (Type your answer in interval notation.) dx S OC. The integral converges because 1 ndj- dx √x +6 S and g(x) are both continuous and positive over the interval 0 g(x) over this interval, the integral of g(x) 1 dx D must be rewritten as has the exact value dx By the Direct Comparison Test, the integral converges because f(x) must be rewritten as 1 The comparison function g(x)= can be used with a comparison test to determine convergence, but since x² Ĵ is not defined. must be rewritten as has a finite value. dx D x+6 must be rewritten as dx . By the Limit Comparison Test, the integral diverges because f(x) +6 f(x) and g(x) are both continuous and positive over the interval .0< lim X-9(x) 00, and the integral of g(x) over
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter39: Symbolism And Algebraic Expressions
Section: Chapter Questions
Problem 5A
Related questions
Question
![Use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integral for convergence. If more
than one method applies, use whatever method you prefer.
S
dx
O B.
√xº
Select the correct choice below and, if necessary, fill in the answer box(es) within your choice.
The comparison function g(x)= can be used with a comparison test to determine convergence, but since
1
3
x° +6
OA. 00
dx
S
0 √x +6 √√x +6
this choice of g(x) is discontinuous at x =
OF
dx
dx
By the Direct Comparison Test, the integral diverges because f(x)
√√x+6
and g(x) are both continuous and positive over the interval, f(x) > g(x) over this interval, and the integral
of g(x) over this interval diverges.
(Type your answer in interval notation.)
1
this choice of g(x) is discontinuous at x =
dx
dx
izlas
-S.
√√x+6
S
0 √√x +6
1
The comparison function g(x)= can be used with a comparison test to determine convergence, but since
S
interval converges, and J
1
ndj-
dx
√√x+6
(Type your answer in interval notation.)
OC. The integral converges because
dx
dx
By the Limit Comparison Test, the integral converges because f(x)
√x +6
and g(x) are both continuous and positive over the interval,0<lim <oo, the integral of g(x) over this
f(x)
g(x)
0
√√x+6
1
this choice of g(x) is discontinuous at x =
1
dx
OR İZİSİ2
OD.
OE. The integral diverges because J
dx
dx
6
√x +6
has a finite value.
The comparison function g(x)= can be used with a comparison test to determine convergence, but since
3
dx
over this interval converges, and
D
(Type your answer in interval notation.)
Ĵ
D
dx
√x° +6
D
+6
this choice of g(x) is discontinuous at x =
dx
ISAA
-S.
dx
dx
By the Direct Comparison Test, the integral converges because f(x)
+6
√xº +6
and g(x) are both continuous and positive over the interval. f(x) > g(x) over this interval, the integral of g(x)
1
dx
dx
√√x² +6
D
must be rewritten as
has the exact value
dx
must be rewritten as
Ĵ
D
1
The comparison function g(x)=
can be used with a comparison test to determine convergence, but since
x²
must be rewritten as
is not defined.
has a finite value.
dx
√√x° +6
must be rewritten as
By the Limit Comparison Test, the integral diverges because f(x)
f(x)
X-9(x) oo, and the integral of g(x) over
√x+6
√x+6
and g(x) are both continuous and positive over the interval,0<lim
this interval diverges.
(Type your answer in interval notation.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb65e1ef9-7834-4c8b-afc0-c44f4ca2e70e%2Fd5651a04-01e7-45ff-90fd-9d4d1fc302b1%2Fag7r8wr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integral for convergence. If more
than one method applies, use whatever method you prefer.
S
dx
O B.
√xº
Select the correct choice below and, if necessary, fill in the answer box(es) within your choice.
The comparison function g(x)= can be used with a comparison test to determine convergence, but since
1
3
x° +6
OA. 00
dx
S
0 √x +6 √√x +6
this choice of g(x) is discontinuous at x =
OF
dx
dx
By the Direct Comparison Test, the integral diverges because f(x)
√√x+6
and g(x) are both continuous and positive over the interval, f(x) > g(x) over this interval, and the integral
of g(x) over this interval diverges.
(Type your answer in interval notation.)
1
this choice of g(x) is discontinuous at x =
dx
dx
izlas
-S.
√√x+6
S
0 √√x +6
1
The comparison function g(x)= can be used with a comparison test to determine convergence, but since
S
interval converges, and J
1
ndj-
dx
√√x+6
(Type your answer in interval notation.)
OC. The integral converges because
dx
dx
By the Limit Comparison Test, the integral converges because f(x)
√x +6
and g(x) are both continuous and positive over the interval,0<lim <oo, the integral of g(x) over this
f(x)
g(x)
0
√√x+6
1
this choice of g(x) is discontinuous at x =
1
dx
OR İZİSİ2
OD.
OE. The integral diverges because J
dx
dx
6
√x +6
has a finite value.
The comparison function g(x)= can be used with a comparison test to determine convergence, but since
3
dx
over this interval converges, and
D
(Type your answer in interval notation.)
Ĵ
D
dx
√x° +6
D
+6
this choice of g(x) is discontinuous at x =
dx
ISAA
-S.
dx
dx
By the Direct Comparison Test, the integral converges because f(x)
+6
√xº +6
and g(x) are both continuous and positive over the interval. f(x) > g(x) over this interval, the integral of g(x)
1
dx
dx
√√x² +6
D
must be rewritten as
has the exact value
dx
must be rewritten as
Ĵ
D
1
The comparison function g(x)=
can be used with a comparison test to determine convergence, but since
x²
must be rewritten as
is not defined.
has a finite value.
dx
√√x° +6
must be rewritten as
By the Limit Comparison Test, the integral diverges because f(x)
f(x)
X-9(x) oo, and the integral of g(x) over
√x+6
√x+6
and g(x) are both continuous and positive over the interval,0<lim
this interval diverges.
(Type your answer in interval notation.)
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