MATH 255 Midterm: MATH 255 McGill Examw07

• School: McGill University
• Department: Mathematics and Statistics
• Course: MATH 255
• Professor: All

Document Summary

This exam comprises the cover and 2 pages with 8 questions. Show that the set c= {c c = a + b: aea be b} is bounded and sup c = sup a + sup b. 3. (a) let a > 0, prove that lim ifa = 1 n~oo (b) let al,a2,. Prove that ak-l, ak be k positive numbers lim (a~ + a~ + n-too n ) l. 4 (a) show that every increasing bounded sequence (ak) is convergent. (b) let f be defined and increasing on the interval (a, b). C e (a, b) we have that lim f and lim f exist. x-+c+ x-+c- 5. (. a) let j be defined on the punctured neighborhood n = {x : 0 < ix -al < a} If lim j(x) = a, prove that j is bounded on a punctured neighborhood x-ta. {x:o