catto - math.ucla.edujhrooney/W18/content/feb01.pdf · Discussion 4 bndinahytmsandapphiahnr...

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Discussion 4 bndinahytmsandapphiahnr February 1,2018 1 Describe the following wnhutiwmhiutowfaus : ¥mht x=rwnl Cglindninl coordinated Cspheimlwudmihst ( III. (a) r=ro (d) p=po aphid (b) 0=00 (e) 0=00 x=psm¢wsO catto a # % &IgwmYfm° (a) cylinder (d) sphere (b) half . plane (e) half . plane (c) higutnlpbme (f) cone @ Find quutmsinyhmilwndinuhrfntheplanetzocamhmlt and thophueofmdiusasoantdatlo ,0,a) . Futheplane , zo=z=pws¢ . Fnttuphm , p=2aws¢ . @ Findttuamugevaheoffex .gr#yrauttudihD=fk.peR4x2tyIaT . Thanafttudishisnei, wthanuyevuhuis t.at#updA=tTazfYToayrrdaradI=aFfoar2dr=I2I . fthusthewuageditunufmapintinthedihtotheoigiismnethmhlfthemdins . ]

Transcript of catto - math.ucla.edujhrooney/W18/content/feb01.pdf · Discussion 4 bndinahytmsandapphiahnr...

Page 1: catto - math.ucla.edujhrooney/W18/content/feb01.pdf · Discussion 4 bndinahytmsandapphiahnr February1,2018 1 Describe the following wnhutiwmhiutowfaus: ¥mht x=rwnl Cglindninl coordinated

Discussion 4bndinahytmsandapphiahnr

February 1,2018

�1� Describe the following wnhutiwmhiutowfaus:

¥mhtx=rwnl

Cglindninlcoordinated Cspheimlwudmihst ( III.

(a) r=ro (d) p=po

aphid

(b) 0=00 (e) 0=00x=psm¢wsOcatto

a # %&IgwmYfm°

(a) cylinder (d) sphere

(b) half . plane (e) half .

plane

(c) higutnlpbme(f) cone

@ Find quutmsinyhmilwndinuhrfntheplanetzocamhmlt and

thophueofmdiusasoantdatlo,0,a) .

Futheplane, zo=z=pws¢ . Fnttuphm, p=2aws¢ .

@ Findttuamugevaheoffex.gr#yrauttudihD=fk.peR4x2tyIaT.

Thanafttudishisnei, wthanuyevuhuis

t.at#updA=tTazfYToayrrdaradI=aFfoar2dr=I2I .

fthusthewuageditunufmapintinthedihtotheoigiismnethmhlfthemdins.]

Page 2: catto - math.ucla.edujhrooney/W18/content/feb01.pdf · Discussion 4 bndinahytmsandapphiahnr February1,2018 1 Describe the following wnhutiwmhiutowfaus: ¥mht x=rwnl Cglindninl coordinated

�4� hlwhte the volume of the"

in cream one

"

bounded

bebwhyzFxEjanlabwebyx7y7zt4.vohme-fMfFYo2p3m4dpd4dO-2itCfFsmodDHo2pdp-lantkHsh-ybgIrdTfthwmwheanirthisisinyhimalamdinahoD@LetRbettunlidbullofnadinsaantudatGoid.bmputoHsEdV.fffsEdV-fYfFfomwkCprwiedfismAdpd01dO.net

V

= 2*fo¥fowHp4ws4sm¢dpd¢

= 64yd fo÷ wsttsiitdp

=¥t€

Page 3: catto - math.ucla.edujhrooney/W18/content/feb01.pdf · Discussion 4 bndinahytmsandapphiahnr February1,2018 1 Describe the following wnhutiwmhiutowfaus: ¥mht x=rwnl Cglindninl coordinated

�6� Let

Rbetteregwnboumhdobwebyttepamboloidz-6-xtjandbehwbytheunez-xFy.hmptufffzzdV.Usinyglindnidwordinethgthemfmsaez-G-r2andz-r.whikinluntwhmr-z-6-r2-sr-2.Thns.fffeav-fohtfoYrtr2zrdIrd0dV-2nfohfrttzrdzdr-nfo2fltFFrifrdr-iTfo2lrEl3r3t36ddr-ftti@hmputettuameyetitmnfumajomtinttuwlidballB-kxiy.zIeR3Ix2ty7EeaYtottubounduyofB.welldothisinphinwlwoulinaty.lfapintqinBhusrphniulwoulinahslpl9d.thmpisthedintmefumttooigintoq.wapisttuditamfumqtothebmdeyofB.Theballhasvohme5tita3wtkaumgevaheisEaEEfoaCa-plp3mAdpd0doe3zHotsm4ddHoalaffldpHFTTT-as.gd.g

÷

Page 4: catto - math.ucla.edujhrooney/W18/content/feb01.pdf · Discussion 4 bndinahytmsandapphiahnr February1,2018 1 Describe the following wnhutiwmhiutowfaus: ¥mht x=rwnl Cglindninl coordinated

@ Find the untnfmamfaanifumnlid hemisphere A of radius a .

We can ammelhetttw hemisphere Issitting onttuxy . planeand centered

on the taxis . By symmetry , ×=j=o ,and

⇐ k¥Ns

Sz DV

= I ME to lpw . Afismcddpdodo

=

at (fo÷ws¢m¢d¢) ( [ pdp)⇒ 4

= £72 T

Page 5: catto - math.ucla.edujhrooney/W18/content/feb01.pdf · Discussion 4 bndinahytmsandapphiahnr February1,2018 1 Describe the following wnhutiwmhiutowfaus: ¥mht x=rwnl Cglindninl coordinated

@ Fmdttnwlumefaballofmdinsauntelatloialbyinhgatginyhniwlwndinaho .

r.¥€??"

that

.es?so.pnxqatdo=2nfF2fow*psin4dpd4u=wsp=lbnF/Psm4ws34dydu=-sm$d0=tbjtIfIu3dn=#Ta