SOLVED: 3. Using the Basic Comparison Test and/or the Limit Comparison Test , determine which ones of the following improper integrals are convergent O1 divergent Do not calculate their value. sin % +

Improper Integrals – Convergence and Divergence – Calculus 2
Improper Integrals – Convergence and Divergence – Calculus 2

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3. Using the Basic Comparison Test and/or the Limit Comparison Test , determine which ones of the following improper integrals are convergent O1 divergent _ Do not calculate their value.
sin % + 2cos % + 10 dx 22
arctan x dx :.l
I -7 d 22 +x+5
sin % dx 11/3
Vz -6
~T2 dx
(f)
10 322 + 5. + 11

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03:56

Determine whether each integral is convergent or divergent: Evaluate those that are convergent. ∫5x dx from 0 to 3-4x, ∫51 dx, ∫x^2 dx, ∫e^2x dx. Use the Comparison Theorem to determine whether the integral ∫x^3+1 sin^2x dx, ∫2x dx, ∫x^2 dx, ∫x^5 dx is convergent or divergent.

05:22

Use the Direct or Limit Comparison Tests to determine if the following improper integrals converge or diverge (don’t evaluate the integrals):

(a)∫(1+cos(6)) dr

(c) ∫[(2+sin(√x))/(√(x-1))] dx

02:14

‘2) Use the Comparison Theorem to determine whether the integral is convergent or divergent_ arctan(x) dx 3 + ex’

08:48

For each of the improper integrals below, if the comparison test applies, enter either A or B followed by one letter from C to K that best applies. If the comparison test does not apply, enter only one possible answer. For example, one possible answer is BF and another one is L.

Hint: 0 < e < 1 for € 21

∫ cos²(€) dxA. The integral is convergentB. The integral is divergentC. by comparison to dzD. by comparison to dzE. by comparison to dzF. by comparison to dzG. by comparison to dzH. by comparison to dzI. by comparison to dzJ. by comparison to dzK. by comparison to dz

∫ (22 + 6) dxA. The integral is convergentB. The integral is divergentC. by comparison to dzD. by comparison to dzE. by comparison to dzF. by comparison to dzG. by comparison to dzH. by comparison to dzI. by comparison to dzJ. by comparison to dzK. by comparison to dz

∫ (16 + 6 sin(x)) dxA. The integral is convergentB. The integral is divergentC. by comparison to dzD. by comparison …

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