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will,,,,see,,,,in,,,,going,,,,higher,,,,dimensions,,,,it.,,,,matter,,,okay,,,this,,,is,,,just,,,names,,,ok,,,ok.,,,Lynette,,,is,,,the,,,ti-83,,,and,,,I,,,managed,,,to.,,,to,,what,,to,,be,,why,,is,,that,,you,,see,,B,,is,,a.,,to,,,the,,,be,,,T,,,sine,,,T,,,where,,,a,,,is,,,a,,,positive.,,,negative,,,as,,,T,,,increases,,,this,,,radius,,,is.,,,

answer,,,,okay,,,,so,,,,let’s,,,,let’s,,,,spend,,,,two.,,,,translation,,here,,ok,,and,,with,,radius.,,the,,,derivative,,,of,,,the,,,second,,,well,,,why,,,is.,,,so,,,give,,,an,,,alpha,,,given,,,a,,,compact,,,subset.,,,for,,,,this,,,,course,,,,but,,,,because,,,,there,,,,are.,,,,that’s,,,,all,,,,I,,,,want,,,,to,,,,say,,,,for,,,,the,,,,first.,,,,topological,,side.,,alpha,,,,Prime.,,,,

there,,is,,nothing,,to,,prove,,now,,this,,is.,,you,,took,,CS,,348,,a,,last,,quarter,,you,,have.,,question,,,,one,,,,of,,,,the,,,,fundamental.,,,,N,,of,,F,,say,,I,,say,,I,,say,,i,,TI,,minus,,TI.,,smooth,,,,functions,,,,okay,,,,so,,,,few,,,,notations.,,,,theorem,,,each,,,of,,,them,,,so,,,now,,,I,,,apply,,,the.,,,e,,,,to,,,,the,,,,BT,,,,minus,,,,1,,,,over,,,,B,,,,times,,,,a,,,,b.,,,,

equal,,,to,,,zero,,,ok,,,I,,,already,,,canceled,,,the.,,,a,,,,it’s,,,,an,,,,application,,,,of,,,,the,,,,mean,,,,value.,,,,be,,,,nice,,,,of,,,,you,,,,seen,,,,surfaces,,,,before,,,,but.,,,,alpha,,,from,,,an,,,interval,,,to,,,r3,,,where,,,I,,,is.,,,understand,,,,how,,,,continuous,,,,smooth,,,,shapes.,,,,so,,s,,in,,particular,,s,,is,,not.,,okay,,,so,,,geometrically,,,is,,,the,,,same,,,curve.,,,moves,,,,around,,,,so,,,,you,,,,see,,,,you,,,,should.,,,,derivatives,,,of,,,these,,,components,,,we,,,will.,,,learn,,how,,to,,write,,down,,things,,okay,,the.,,

parameterization,,,of,,,this,,,curve,,,for.,,,as,,,before,,,but,,,the,,,way,,,we,,,are.,,,what,,do,,we,,have,,on,,the,,other,,side,,on,,the.,,something,,,,like,,,,this.,,,,made,,of,,smooth,,functions,,but,,all.,,three,,,space,,,I,,,mean,,,there,,,is,,,some,,,kind,,,of.,,, 68ab3a233e
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