- 1、本文档共6页,可阅读全部内容。
- 2、原创力文档(book118)网站文档一经付费(服务费),不意味着购买了该文档的版权,仅供个人/单位学习、研究之用,不得用于商业用途,未经授权,严禁复制、发行、汇编、翻译或者网络传播等,侵权必究。
- 3、本站所有内容均由合作方或网友上传,本站不对文档的完整性、权威性及其观点立场正确性做任何保证或承诺!文档内容仅供研究参考,付费前请自行鉴别。如您付费,意味着您自己接受本站规则且自行承担风险,本站不退款、不进行额外附加服务;查看《如何避免下载的几个坑》。如果您已付费下载过本站文档,您可以点击 这里二次下载。
- 4、如文档侵犯商业秘密、侵犯著作权、侵犯人身权等,请点击“版权申诉”(推荐),也可以打举报电话:400-050-0827(电话支持时间:9:00-18:30)。
- 5、该文档为VIP文档,如果想要下载,成为VIP会员后,下载免费。
- 6、成为VIP后,下载本文档将扣除1次下载权益。下载后,不支持退款、换文档。如有疑问请联系我们。
- 7、成为VIP后,您将拥有八大权益,权益包括:VIP文档下载权益、阅读免打扰、文档格式转换、高级专利检索、专属身份标志、高级客服、多端互通、版权登记。
- 8、VIP文档为合作方或网友上传,每下载1次, 网站将根据用户上传文档的质量评分、类型等,对文档贡献者给予高额补贴、流量扶持。如果你也想贡献VIP文档。上传文档
查看更多
And now for something comple y different ...
B) Approximating Areas and Distances
1) Approximating Area under a Curve by Riemann
Sums with sub-intervals
Consider the graph of .
We wish to approximate the area under this curve
and above the x-axis from
To do this, we will find two numbers (an upper
bound and a lower bound) between which this area
must fall. This will involve the use of “upper” and
“lower” rectangles. Let’s see what this is all about!
Break-up #1: Split into 4 equal sub-intervals.
How wide is each interval? Show all work.
Upper Rectangle Case: to use upper rectangles to
approximate the area under the curve, which
endpoint of each interval must be used in this case?
Will this area be an over- or under-estimation of the
true area?
We shall proceed with the solution both specifically
and generally (split your page); very shortly, we will
just use the general solution to save a ton of time!
The upper rectangle solution ...
Lower Rectangle Case: to use lower rectangles to
approximate the area under the curve, which
endpoint of each interval must be used in this case?
Will this area be an over- or under-estimation of the
true area?
We shall proceed with the solution both specifically
and generally. The lower rectangle solution ...
The interval in which the true area must fall is ...
But ... this is not good enough for the boss!
She wants more precision (ie. a smaller interval in
which the true area must fall!!). She wants a
“better” approximation.
So ... what could we do?
Break-up #2: Split into 8 equal sub-intervals.
How wide is each interval? Show all work.
Upper Rectangle Case: use a general solution
Lower Rectangle Case: use a general solution
The more precise (ie. smaller) interval in which the
true area must fall is now ...
But ... this is still not good enough for the boss.
She is very demanding!!
1亿VIP精品文档
相关文档
最近下载
- 0967.新人教版三年级数学下册第二课 长方形、正方形面积的计算(教案)(优秀教学设计)(国家级一等奖、适合公开课).doc
- 新产品立项申请书(标准版).docx VIP
- 梁山伯与祝英台 - 小提琴独奏谱 - 完整乐谱.pdf
- 《妇产科护理》教学教案—产褥.docx VIP
- 黑布林The Adventures of Tom Sawyer汤姆·索亚历险记名著整理.docx
- 生命科学竞赛科学探究类申报书 .pdf
- 住院医师规培考试一阶段内科内分泌病例分析题及辅助检查题.doc
- 部编版七年级语文上册第7课《散文诗二首》教学课件.pptx
- 企业化班级管理在提高中职学生职业素养中的应用——以中职学校与联想校企合作班为例-来源:现代职业教育(高职高专)(第2020004期)-山西教育教辅传媒集团有限责任公司.pdf VIP
- 小学语文作业设计专题讲座.pptx
文档评论(0)