Use the divergence theorem to evaluate s f · ds, where f(x, y, z) = z2xi + y3 3 + tan z j + (x2z + y2)k and s is the top half of the sphere x2 + y2 + z2 = 9. (hint: note that s is not a closed surface. first compute integrals over s1 and s2, where s1 is the disk x2 + y2 ≤ 9, oriented downward, and s2 = s1 ∪ s.)

Yuto and hila attempted to solve the same inequality. their work is shown below. which statement is true about the work shown above? yuto is correct because he isolated the variable correctly and reversed the inequality symbol. yuto is incorrect because he should not have reversed the inequality symbol. hila is correct because she isolated the variable correctly and reversed the inequality symbol. hila is incorrect because she should not have reversed the inequality symbol.