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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 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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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. 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.)
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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