{"id":1512,"date":"2017-11-20T16:21:19","date_gmt":"2017-11-20T21:21:19","guid":{"rendered":"http:\/\/blog.richmond.edu\/math320\/?p=1512"},"modified":"2017-11-20T16:24:25","modified_gmt":"2017-11-20T21:24:25","slug":"muddiest-point-111917","status":"publish","type":"post","link":"https:\/\/blog.richmond.edu\/math320\/2017\/11\/20\/muddiest-point-111917\/","title":{"rendered":"Muddiest Point 11\/16\/17"},"content":{"rendered":"

Upper and Lower Sums<\/h3>\n

We illustrated lower sums in class to show that, given a function \"f\" that is bounded on \"[a,b]\", \"L(f,[a,b],Q)\geq where \"Q\" is a refinement of a given partition \"P\" of \"[a,b]\". This post shows the analogous graph for upper sums that we did not draw in class.<\/p>\n

\"\"<\/a><\/p>\n

These are our observations about the areas in the upper sum and lower sum:<\/p>\n

    \n
  1. \"L(f,[a,b],Q)\geq<\/li>\n
  2. \"U(f,[a,b],Q)\leq<\/li>\n
  3. \"L(f[a,b],P)\leq<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

    Upper and Lower Sums We illustrated lower sums in class to show that, given a function that is bounded on , where is a refinement of a given partition of . This post shows the analogous graph for upper sums that we did not draw in class. These are our observations about the areas in […]<\/p>\n","protected":false},"author":3528,"featured_media":1534,"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":[58822],"tags":[],"class_list":["post-1512","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-muddiest-point"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/blog.richmond.edu\/math320\/files\/2017\/11\/Analysis.jpg?fit=3264%2C2001&ssl=1","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p7L4E1-oo","jetpack-related-posts":[],"_links":{"self":[{"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/posts\/1512","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\/3528"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/comments?post=1512"}],"version-history":[{"count":0,"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/posts\/1512\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/media\/1534"}],"wp:attachment":[{"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/media?parent=1512"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/categories?post=1512"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.richmond.edu\/math320\/wp-json\/wp\/v2\/tags?post=1512"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}