Question

(3 points) For each of the following improper integrals, carefully use the comparison test to decide if the integral converges or diverges. All of your 'similar integrands' should be in the form 1/x” for some power p. 2x 1. dx x3 + 1 A similar integrand whose behaviour is known is A. converges B. diverges , so we find that this integral x +4 2. dx x6 - x A similar integrand whose behaviour is known is A. converges B. diverges so we find that this integral 1 + sin(x) 3. x2 , so we find that this integral A similar integrand whose behaviour is known is O A. converges OB. diverges

Answer 1

0 1 20 de x3 4 2u at olu- x3+1 let fruga 2 x2 No. Here 2x 2 L for al x3+1 x2 Mow, 2 How, 22 du is convergent Se de se convergent when nos, & here n=2 which is greater than 1. thence by comparison test, the given integral is als also convergent 2 + 4 du S 614) x + 4 з я! - Holz X. S to divergent Ste de installivergent (since, here nal; not greater than 17 It sina S dr 25x2 Itdnu dow) 3S 22 2 het flur 23 there 18 (1) 12 Hal for nyl * Idris divergent S 1t dine du udivergent x43 35u² Cance = x, which is less than 1) Sinces frag du -S