Upload
teachopensource
View
219
Download
0
Embed Size (px)
Citation preview
8/9/2019 riemannsums_byu
1/6
Qi{{iuigO'RMztS
IQLifltft|IM
C}'\ntmfdbi
19/=8/91
U}j{jge I||jegcdg{? ]jdcigg \tc|
[nd ]jdcigg |tc j| i cd{n`kh`} iqq}`~jci{jge{nd i}di tgkd}gdi{n{nd
lt}xd `h i e}iqn' [nd iqq}`~jci{j`g| `h {nd i}di|& `} jg{de}if|& {ibd h`}c| `h
}dl{igefd|' [nd |tc j| kdhjgdk i|? & und}d j| {nd ujk{n `h {nd
}dl{igefd|igk i}d{nd~xiftd|und}d{ndndjen{|`h{ndlt}xd|i}d{ibdg&unjln
j|mi|jliffz{ndndjen{`h{ndiqq}`~jci{jge}dl{igefd|'[ndujk{n`h{nd}dl{igefd&`}
& lig md h`tgk mz lifltfi{jge und}d {nd jg{d}xif jg unjln {nd i}di j|
lifltfi{dk j|Ri& mSigk {nd gtcmd} `h |tmjg{d}xif| j| g' [nd}d i}d {n}dd{zqd| `h
]jdcigg\tc|?fdh{nigk&}jen{nigkigkcjkq`jg{'Jgikkj{j`g&{nd}di}d]jdcigg
\tcfjbd cd{n`k| liffdk {nd [}iqd `jkif ]tfd igk \jcq|`g| ]tfd' Iff `h {nd|d
cd{n`k|ujffmdkj|lt||dkjg{nj|d||iz'
[nd fdh{ nigk iqq}`~jci{j`g& if| liffdk fdh{ dgkq`jg{ iqq}`~jci{j`g& j| i
]jdcigg\tc| iqq}`~jci{j`gund}d j| ln`|dg {` md {ndfdh{ dgkq`jg{ `h diln
|tmjg{d}xif&|` '[nd}dh`}d{ndfdh{nigk|tcj|kdhjgdki| '
D~icqfd?
8/9/2019 riemannsums_byu
2/6
G`{d?Jg{nj|d~icqfd&{ndfdh{nigk|tcj|igtgkd}d|{jci{j`g`h{nde}iqn
`gR1&4S
[nd}jen{nigkiqq}`~jci{j`gj|und}d j|ln`|dg{`md{nd}jen{dgkq`jg{
`h diln |tmjg{d}xif& {nd}dh`}d ' Mz kdhjgj{j`g& {nd }jen{ nigk |tc&
'
D~icqfd?
8/9/2019 riemannsums_byu
3/6
G`{d? Jg {nj| d~icqfd& {nd }jen{ nigk |tc j| ig `xd}d|{jci{d `h {nd i}di
tgkd} {nd lt}xd& tgfjbd {nd fdh{ nigk iqq}`~jci{j`g& unjln ejxd| t| ig
tgkd}d|{jci{d'Udlig|tcci}j d{ni{{nd}jen{nik|tciqq}`~jci{j`gejxd|ig
`xd}d|{jci{d undg{nd lt}xdj|kdl}di|jgeigk ejxd| ig tgkd}d|{jci{d undg{nd
lt}xdj|jgl}di|jge'[nd`qq`|j{diqqfjd|{`{ndfdh{nigk|jkd|tc|'
Ig`{nd}]jdcigg\tcCd{n`kj|{ndcjkq`jg{iqq}`~jci{j`gcd{n`k'[nd
cjkq`jg{iqq}`~jci{j`gj|kdhjgdkmz und}d j|
{ndcjkq`jg{`h '
[nd{}iqd `jkif iqq}`~jci{j`g t|d|{}iqd `jk| {` d|{jci{d {nd i}di tgkd}
{nd lt}xd jg|{dik `h }dl{igefd|' [nd [}iqd `jkif ]tfd j| kd|l}jmdk mz?
'
[nd\jcq|`g|]tfdj|i}tfd`hiqq}`~jci{j`g`hi}dit|jgeqi}im`fi|jg|{dik
`h }dl{igefd| `} {}iqd `jk|' [nd kdhjgj{j`g `h {nd \jcq|`g| ]tfd j|?
Cjkq`jg{Iqq}`~jci{j`g [}iqd `jkifIqq}`~jci{j`g
8/9/2019 riemannsums_byu
4/6
' [nd
\jcq|`g]tfd`gfzu`}b|jh und}dgj|igdxdgjg{ded}'
D^ICQFD? H`} {nd lt}xd & {nd i}di tgkd} {nd lt}xd jg {nd lf`|dk
jg{d}xif R1&91S j| kd|l}jmdk mz unjln dytif| {` 989'=4 |yti}d tgj{|'
Mdf`ui}d{ndiqq}`~jci{j`g|t|jge]jdcigg\tc|?
g Fg ]g Cg [g \jcq|`g| = ;;'18
8/9/2019 riemannsums_byu
5/6
G@[D?[n`ten{ndgtcmd}`h|tmjg{d}xif|j|`gfz=&{nd\jcq|`g|Cd{n`kejxd|i
xd}zillt}i{diqq}`~jci{j`g`hi}ditgkd}{ndlt}xd'
\jcq| g|]tfd{t}g|`t{{`md{ndmd|{iqq}`~jci{j`g`h{ndi}ditgkd}{nd
lt}xd|jgldj{|kdxji{j`gh}`c{nd{}tdi}dij|{ndfdi|{'Jg{nj|d~icqfd&j{|kdxji{j`g
j|1h`} iffxiftd| `hg'[nd |dl gkmd|{iqq}`~jci{j g`h{ndi}dij| {ndcjkq`jg{
iqq}`~jci{j`g cd{n`k& igk {nd {nj}k j|{nd{}iqd jkif cd{n`k' [n}`ten ht}{nd}
d~qd}jcdg{i{j`g& j{ j| q}`xdk {ni{ g` ci{{d} uni{ l`glixj{z `}
jgl}di|jge/kdl}di|jgemdnixj`}`h{ndlt}xdj|&{ndmd|{iqq}`~jci{j`gujffmd{nd
\jcq|`g|Cd{n`k'
8/9/2019 riemannsums_byu
6/6
\`t}ld|?
n{{q?//qd`qfd'n`h|{}i'dkt/\{dhigPUigd}/}difu`}fk/jg{de}if/gtcjg{'n{cf
n{{q?//ci{nu`}fk'u`fh}ic'l`c/
E}iqn?
n{{q?//uuu'|ft'dkt/lfi||d|/cizcb/]jdcigg/]jdcigg'n{cf