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.

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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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
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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