For each of the improper integrals below, if the comparison test applies, enter

Question

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, and if the comparison test does not apply, enter only L. For example, one possible answer is BF, and another one is L. 1. integral^infinity_1 cos^2 (x)/x^+ 3 dx 2. integral^infinity_1 10 + sin (x)/Squareroot x - 0.2 dx 3. integral^infinity_1 e^-x/x^2 dx 4. integral^infinity_1 x/Squareroot x^6 + 3 dx A. The integral is convergent B. The integral is divergent C. by comparison to integral^infinity_1 1/x^2 - 3 dx. D. by comparison to integral^infinity_1 1/x^2 + 3 dx. E. by comparison to integral^infinity_1 cos^2 (x)/x^2 dx. F. by comparison to integral^infinity_1 e^x/x^2 dx. G. by comparison to integral^infinity_1 -e^-x/2x dx. H. by comparison to integral^infinity_1 1/Squareroot x dx. I. by comparison to integral^infinity_1 1/Squareroot x^5 dx. J. by comparison to integral^infinity_1 1/x^2 dx. K. by comparison to integral^infinity_1 1/x^3 dx. L. The comparison test does not apply.

Explanation / Answer

1) This integral is smaller than the integral given in part D. And we know that the integral given in part D is larger than this integral and converges. Therefore, correct answer to this part is AD

2) We know that integral given in part H is smaller than this integra and diverges. Therefore, by comparison this integral diverges too. Hence, the correct choice would be BH

3) There doesn't seem to be an appropriate comparison to this integral. Therefore, I would enter L

4) This integral is smaller than the integral in part J and we know that integral in part J converges. Therefore, this integral converges too. Hence, correct choice is AJ

5) This integral is smaller than the integral in part J and we know that integral in part J converges. Therefore, this integral converges too. Hence, correct choice is AJ

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.