Analise Matematica

■♥st✐t✉t♦ ❙✉♣❡r✐♦r ❞❡ ❊♥❣❡♥❤❛r✐❛ ❞❡ ❈♦✐♠❜r❛
❆♥á❧✐s❡ ▼❛t❡♠át✐❝❛ ■

❆♣♦♥t❛♠❡♥t♦s ❞❡ ❈á❧❝✉❧♦ ■♥t❡❣r❛❧

❆✉t♦r✿
❏♦r❣❡

❙✉♣❡r✈✐s♦r✿

❈r✉③

❉r❛✳ ❊♠í❧✐❛

✾ ❞❡ ▼❛✐♦ ❞❡ ✷✵✶✹

❇✐❣♦tt❡

Pr❡❢á❝✐♦ ❡ ❆❣r❛❞❡❝✐♠❡♥t♦s
❈♦♠♦ ❡✉ ♠❡ ♠❡t✐ ♥✐st♦❄
◆♦ ♠❡✉ ♣❡r❝✉rs♦ ❛❝❛❞é♠✐❝♦✱ ❛ss✐♠✐❧❡✐ ❛s ❞✐✜❝✉❧❞❛❞❡s s❡♥t✐❞❛s ♣♦r ♠✉✐t♦s ❝♦❧❡❣❛s q✉❛♥t♦ à ♠❛tér✐❛ ❧❡❝✐♦♥❛❞❛
❡♠ ❆♥á❧✐s❡ ▼❛t❡♠át✐❝❛ ■✱ ♣❡❧♦ q✉❡ ♣♦♥❞❡r❡✐ ❞❡♥tr♦ ❞❛s ♠✐♥❤❛s ♣♦ss✐❜✐❧✐❞❛❞❡s✱ ❝♦♥tr✐❜✉✐r ♣❛r❛ ✉♠ ♠❡❧❤♦r s✉❝❡ss♦
❛❝❛❞é♠✐❝♦✳
❍❡s✐t❡✐ ❝♦♥t✉❞♦✱ ❡♠ ♠❡ ❛✈❡♥t✉r❛r ❛ ✧r❡s♦❧✈❡r✧❡ ❝♦♠♣✐❧❛r ♦s ❡①❡r❝í❝✐♦s ✐♥❝❧✉í❞♦s ♥❡st❡ ♠❛♥✉❛❧✱ ♠❛s ❛ ❉r❛✳ ❊♠í❧✐❛
❇✐❣♦tt❡ ❞❡s❞❡ ❧♦❣♦ ❡♥t❡♥❞❡✉ ❡ ❛♣♦✐♦✉ ❛ ♠✐♥❤❛ ✐❞❡✐❛ ❡ ✐♥t❡❣r♦✉✲❛ ♥♦ ♣r♦❥❡t♦ ❞❡ ✈♦❧✉♥t❛r✐❛❞♦ ❞♦ ■P❈✳
❖s ❡①❡♠♣❧♦s ❞♦s ❡①❡r❝í❝✐♦s r❡s♦❧✈✐❞♦s✱ r❡tr❛t❛❞♦s ♥♦ ♣r❡s❡♥t❡ ♠❛♥✉❛❧ ❝♦♥st✐t✉❡♠ ✉♠ ❝♦♠♣❧❡♠❡♥t♦ às ♠❛tér✐❛s
❧❡❝✐♦♥❛❞❛s ♥❛ ✉♥✐❞❛❞❡ ❝✉rr✐❝✉❧❛r✳
◆♦ ❢✉♥❞♦✱ ❝♦♠ ❡st❡ ♠❛♥✉❛❧ ♣r❡t❡♥❞♦ ♣♦r ✉♠ ❧❛❞♦ ❛❣r❛❞❡❝❡r às ♣❡ss♦❛s q✉❡ ❝♦♥tr✐❜✉ír❛♠ ♣❛r❛ ♦ ♠❡✉ s✉❝❡ss♦
♥❡st❛ ❯❈✱ ♥♦♠❡❛❞❛♠❡♥t❡✱ ❛ ❉r❛✳

❊♠í❧✐❛ ❇✐❣♦tt❡ ✭❉♦❝❡♥t❡ ❯❈✮✱ ❛ ❉r❛✳

❊♠í❧✐❛ ❋❡rr❡✐r❛ ✭❋✐❣✉❡✐r❛ ❞❛ ❋♦③✮ ❡ ❛

❉r❛✳ ❆♥❛ ▼❛r✐❛ ❙✐❧✈❛ ✭▲✐❝❡♥❝✐❛t✉r❛ ▼❛t❡♠át✐❝❛ ✲ ✈✐❛ ❊♥s✐♥♦✮ ♣♦r t♦❞♦ ♦ ❛♣♦✐♦ ❞❛❞♦ ❝♦♠♦ t❡①t♦s ♠❛t❡♠át✐❝♦s✱
❢r❡q✉ê♥❝✐❛s✱ ❛♣♦♥t❛♠❡♥t♦s✱ ❧✐✈r♦s✱ ❡t❝✳✳✱ ❜❡♠ ❝♦♠♦ ❛ t♦❞♦s ♦s ✭❡①✮❝♦❧❡❣❛s ❞♦ ❊❈❙ ✭♣r✐♥❝✐♣❛❧♠❡♥t❡ ♦s ❛♥t✐✲❝❤✐♥❛s
❞♦s ❇❛❞❇♦②s ❡ ♦s ▲②♥❝❡●❛♠❡rs✮ q✉❡ ❝♦♠✐❣♦ tê♠ ♣❛rt✐❧❤❛❞♦ ❛ ❛✈❡♥t✉r❛ ❛❝❛❞é♠✐❝❛✳ ❊✱ ♣♦r ♦✉tr♦ ❧❛❞♦✱ ❞❛r ♦ ♠❡✉
❝♦♥tr✐❜✉t♦ à ❝♦♠✉♥✐❞❛❞❡ ❡st✉❞❛♥t✐❧ ❞❡st❛ ✉♥✐❞❛❞❡ ❝✉rr✐❝✉❧❛r✳

❆●❘❆❉❊❈■▼❊◆❚❖❙ ❊❙P❊❈■❆■❙ ❉❊

❏♦r❣❡ ▼✐❣✉❡❧ ❆♥t✉♥❡s ❞❛ ❈r✉③
❛❧✉♥♦ ♥

♦

✷✶✶✾✵✹✽✻ ✭❊❈❙✮

✲ ❛♦ ❣❛♥❣✉❡ ❞♦s ❇❛❞❇♦②s ❝♦♠♣♦st♦ ♣♦r ①♦✉r✐ç♦ ✭❙❆P✮✱ ❙♦❛r❡s ✭❊♠✐❣r❛♥t❡ ❆❧❡♠ã♦✮✱ ❈❛❜r✐t❛ ✭♠❡✉ ♣❛❞r✐♥❤♦ ❡ ❛t✉❛❧♠❡♥t❡
❆❋❑ ♥♦ ❣r✉♣♦✮✱ ▲✉✐s✐♥❤♦ ✭▼♦♥s✐❡✉r ❋❛✐s♦♥ ✰ ❙❊❈✮ ❡ ❘✐❝❛r❞♦ ◆❡t♦ ✭❆❊ ■❙❊❈✮✳ ❱♦❝ês ❝♦♥s❡❣✉✐r❛♠ ♦ ✐♠♣♦ssí✈❡❧✱ q✉❡ ❡r❛
♠✉❞❛r ♦ ❏♦r❣❡✳ P♦❞❡♠ ♥ã♦ ♥♦t❛r✱ ♠❛s ✜③❡r❛♠✲♦✱ ♣♦r ✐ss♦✱ ❖ ▼❊❯ ▼❯■❚❖ ❖❇❘■●❆❉❖ ❞♦ ❢✉♥❞♦ ❞♦ ❝♦r❛çã♦✦
✲ ❛♦ ❙❡♥❤♦r ❏♦❛q✉✐♠ ❆♥t✉♥❡s ✭❆✈ô✮ ♣♦r t♦❞♦s ♦s ✈♦t♦s ❞❡ ♣❡rs❡✈❡r❛♥ç❛✴❝♦♥✜❛♥ç❛✴✐♥s♣✐r❛çã♦ ❡ ♣♦r ♥♦s t❡r ❝♦♥❞✉③✐❞♦ ♥✉♠
❝❛♠✐♥❤♦ ❞❛