MATH 355 Final: MATH 355 Amherst S14M355FinalPart2

• School: Amherst College
• Department: Mathematics and Statistics
• Course: MATH 355
• Professor: All

Document Summary

Due friday may 9th 5pm at my o ce. This is your personal copy do not distribute. Complete two problems: suppose that a1, a2, . , an are all positive real numbers (ai > 0 for i {1, 2, . , n}). (a) prove that if a1 a2 an = 1 then a1 + a2 + + an n. (b) use your result from (a) to show that. N a1 a2 an a1 + a2 + + an n. Prove that f is continuous. (i) let f, g : [a, b] r be continuous functions that are di erentiable on (a, b) with g 6= 0 on (a, b). Suppose that the function h1(x) = f (x)/g (x) is increasing on (a, b). 1 xq that the inequality xp 1 p > xq 1 q holds for x (1, ): if you complete this problem choose either (a) or (b) and not both.