{"id":1552,"date":"2017-11-21T12:21:53","date_gmt":"2017-11-21T17:21:53","guid":{"rendered":"http:\/\/blog.richmond.edu\/math320\/?p=1552"},"modified":"2017-11-26T12:33:49","modified_gmt":"2017-11-26T17:33:49","slug":"weekly-challenge-hw9-2abc","status":"publish","type":"post","link":"https:\/\/blog.richmond.edu\/math320\/2017\/11\/21\/weekly-challenge-hw9-2abc\/","title":{"rendered":"HW 9: Challenge 2(a,b,c)"},"content":{"rendered":"

Tongzhou, 11\/21<\/em><\/p>\n

(a) Since \"L(h,P)=\sum_{k=1}^n \"m_k\" needed to be determined firstly.<\/p>\n

By definition, \"m_k.<\/p>\n

Since \"[x_{k-1},x_k]\" is any partition of \"[0,1]\", \"m_k<\/p>\n

Therefore, \"L(h,P).<\/p>\n

(b) Sidework: I want to have \"U(h,P) which means \"1(x_k-0)+2(1-x_k)<1+1\/10.\" I want to determine how far \"x_k\" could be away from \"1\".<\/p>\n

Thus \"lim_{k so that \"1-x_k.<\/p>\n

Now choose \"P=. Again I need to determine \"M_k\" before I find \"U(h,P)\".<\/p>\n

\"M_1.<\/p>\n

\"U(h,P)=<\/p>\n

(c) By the intuition of (b).<\/em><\/p>\n

Let \"\epsilon>0\", Choose \"P_\epsilon<\/p>\n

\"M_1.<\/p>\n

\"U(h,P_\epsilon).<\/p>\n","protected":false},"excerpt":{"rendered":"

Tongzhou, 11\/21 (a) Since needed to be determined firstly. By definition, . Since is any partition of , Therefore, . (b) Sidework: I want to have which means I want to determine how far could be away from . Thus so that . Now choose . Again I need to determine before I find . […]<\/p>\n","protected":false},"author":3535,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[58827],"tags":[],"class_list":["post-1552","post","type-post","status-publish","format-standard","hentry","category-challenge-solutions"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p7L4E1-p2","jetpack-related-posts":[],"_links":{"self":[{"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/posts\/1552","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/users\/3535"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/comments?post=1552"}],"version-history":[{"count":0,"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/posts\/1552\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/media?parent=1552"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/categories?post=1552"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/tags?post=1552"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}