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 dx x3 +6 4 ... Choose the correct answer below. O A. dx diverges because 0s +6 1 1 By the Direct Comparison Method, on [4, co) and x° +6 4 00 1 dx diverges. 4 В. dx 1 1 By the Direct Comparison Method, converges because 0s on [4, 0) and x3 +6 4 x° +6 00 1 dx converges. 4 OC. 1/ (x³ + 6) dx diverges because lim x3 By the Limit Comparison Test, = 1 and xp- +6 1/x3 4 4 diverges. O D. The integral cannot be evaluated using integration, so the integral diverges.
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 dx x3 +6 4 ... Choose the correct answer below. O A. dx diverges because 0s +6 1 1 By the Direct Comparison Method, on [4, co) and x° +6 4 00 1 dx diverges. 4 В. dx 1 1 By the Direct Comparison Method, converges because 0s on [4, 0) and x3 +6 4 x° +6 00 1 dx converges. 4 OC. 1/ (x³ + 6) dx diverges because lim x3 By the Limit Comparison Test, = 1 and xp- +6 1/x3 4 4 diverges. O D. The integral cannot be evaluated using integration, so the integral diverges.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 93E
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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.
00
dx
x3 +6
...
Choose the correct answer below.
O A.
dx
diverges because 0s
1
1
By the Direct Comparison Method,
on [4, 0) and
x3 + 6
x3 +6
1
dx diverges.
4
В.
00
dx
1
1
By the Direct Comparison Method,
converges because 0s
3
on [4, co) and
x3 +6
4
x° + 6
dx converges.
С.
00
dx
diverges because lim
1/ (x³ + 6)
1
= 1 and
By the Limit Comparison Test,
x° + 6
4
1/x3
4
diverges.
D. The integral cannot be evaluated using integration, so the integral diverges.
8
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