❈➪▲❈❯▲❖✿ ❯▼❆ P❘❖P❖❙❚❆ P❖❙❙❮❱❊▲ P❆❘❆ ❖
❊◆❙■◆❖ ▼➱❉■❖
❑➱▲■❆ ❘❖❉❘■●❯❊❙ ❉❊ ◗❯❊■❘❖❩ ❙❖❯❩❆
▼❡str❛❞♦ Pr♦✜ss✐♦♥❛❧ ❡♠ ▼❛t❡♠át✐❝❛ ❡♠ ❘❡❞❡ ◆❛❝✐♦♥❛❧
P❘❖❋▼❆❚✴❯❋▼❚
❈➪▲❈❯▲❖✿ ❯▼❆ P❘❖P❖❙❚❆ P❖❙❙❮❱❊▲ P❆❘❆ ❖
❊◆❙■◆❖ ▼➱❉■❖
❑é❧✐❛ ❘♦❞r✐❣✉❡s ❞❡ ◗✉❡✐r♦③ ❙♦✉s❛
❉✐ss❡rt❛çã♦ s✉❜♠❡t✐❞❛ à ❈♦♦r❞❡♥❛çã♦ ❞♦ ❈✉rs♦ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ▼❛t❡♠át✐❝❛✱ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼❛t♦ ●r♦ss♦✱ ❝♦♠♦ r❡✲ q✉✐s✐t♦ ♣❛r❝✐❛❧ ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ ❣r❛✉ ❞❡ ▼❡str❡ ❡♠ ❊♥s✐♥♦ ❞❡ ▼❛t❡♠át✐❝❛✳
❖r✐❡♥t❛❞♦r✿
Pr♦❢✳ ❉r✳ ❈❛r❧♦s ❘♦❞r✐❣✉❡s ❞❛ ❙✐❧✈❛
❙♦✉s❛✱ ❑é❧✐❛ ❘♦❞r✐❣✉❡s ❞❡ ◗✉❡✐r♦③
❈á❧❝✉❧♦✿ ✉♠❛ ♣r♦♣♦st❛ ♣♦ssí✈❡❧ ♣❛r❛ ♦ ❡♥s✐♥♦ ♠é❞✐♦ ❑é❧✐❛ ❘♦❞r✐❣✉❡s ❞❡ ◗✉❡✐r♦③ ❙♦✉s❛ ✕ ✷✵✶✹
✾✼❢✳✿ ✐❜❧✳
❖r✐❡♥t❛❞♦r✿ Pr♦❢♦✳ ❉r✳ ❈❛r❧♦s ❘♦❞r✐❣✉❡s ❞❛ ❙✐❧✈❛✳
❉✐ss❡rt❛çã♦ ✭▼❡str❛❞♦ Pr♦✜ss✐♦♥❛❧ ❡♠ ▼❛t❡♠át✐❝❛ ❡♠ ❘❡❞❡ ◆❛❝✐♦♥❛❧✮ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼❛t♦ ●r♦ss♦✱ ❇❛rr❛ ❞♦ ●❛rç❛s✱ ✷✵✶✹✳
❆❣r❛❞❡❝✐♠❡♥t♦s
➚ ❉❡✉s✱ ♣♦r ♠❡ ♣r♦♣♦r❝✐♦♥❛r ♠❛✐s ❡st❛ ❝♦♥q✉✐st❛✳
❆♦ ♠❡✉ ❡s♣♦s♦✱ ❊❧✐❛♥❞r♦✱ ♣❡❧♦ ❝♦♠♣❛♥❤❡✐r✐s♠♦ ♥❡st❡s ❞♦✐s ❛♥♦s ❞❡ ♠✉✐t❛ ❞❡✲ ❞✐❝❛çã♦✳
❆♦s ♠❡♠❜r♦s ❞❛ ❜❛♥❝❛ ❞❡ ❛✈❛❧✐❛çã♦✱ ❝✉❥❛s s✉❣❡stõ❡s ❡♥❣r❛♥❞❡❝❡r❛♠ ♦ tr❛❜❛❧❤♦✳ ❊♠ ❡s♣❡❝✐❛❧ ❛♦ ♣r♦❢❡ss♦r ❈❛r❧♦s✱ ♣❡❧❛s ❞✐s❝✉ssõ❡s ❡ ♣❡❧♦ ❞✐r❡❝✐♦♥❛♠❡♥t♦ ❞♦ tr❛❜❛❧❤♦✳
❆♦s ❝♦❧❡❣❛s ❡ ❛♦s ♣r♦❢❡ss♦r❡s ❞♦ P❘❖❋▼❆❚✱ ♣❡❧♦s ❡♥s✐♥❛♠❡♥t♦s ❡ ♣❡❧❛s ❞✐s✲ ❝✉ssõ❡s q✉❡ ♠✉✐t♦ ♠❡ ❡♥r✐q✉❡❝❡r❛♠✳
❆♦s✱ ❞✐r❡t♦r❡s ❆❧❡①❛♥❞r❡ ❡ ❱❡r❛❧✐❝❡✱ ♣❡❧♦ ✐♥❝❡♥t✐✈♦ ♥♦s ♠♦♠❡♥t♦s ❞❡ ❞❡sâ♥✐♠♦✳ ❆♦s ❝♦❧❡❣❛s ❞♦ P❘❖❋▼❆❚ ❞❛ t✉r♠❛ ❞❡ ✷✵✶✷ ❞❛ ❯❋❚▼ ♣❡❧♦ ❝♦♥✈í✈✐♦ ❡ ♣♦r t♦❞❛s ❛s tr♦❝❛s ❞❡ ❡①♣❡r✐ê♥❝✐❛s q✉❡ ❝♦♥tr✐❜✉ír❛♠ ❛✐♥❞❛ ♠❛✐s ♣❛r❛ ❛ ♠✐♥❤❛ ❢♦r♠❛çã♦ ❞♦❝❡♥t❡✳
➚ ❈❆P❊❙ ♣❡❧♦ ❛♣♦✐♦ ✜♥❛♥❝❡✐r♦ ❡ à ❙♦❝✐❡❞❛❞❡ ❇r❛s✐❧❡✐r❛ ❞❡ ▼❛t❡♠át✐❝❛ ♣❡❧❛ ❝r✐❛çã♦ ❡ ✐♠♣❧❛♥t❛çã♦ ❞♦ P❘❖❋▼❆❚ ♥♦ ❇r❛s✐❧✳
❘❡s✉♠♦
❖ ❡st✉❞♦ ❞♦ ❈á❧❝✉❧♦ ❉✐❢❡r❡♥❝✐❛❧ ❡ ■♥t❡❣r❛❧ é ❝♦♥s✐❞❡r❛❞♦ ✉♠ ❞♦s ❝♦♥t❡ú❞♦s ♠❛t❡♠á✲ t✐❝♦s ♠❛✐s ✐♥✢✉❡♥t❡s ♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❝✐❡♥tí✜❝♦ ❡ t❡❝♥♦❧ó❣✐❝♦ ❛t✉❛❧✳ P❡r♠✐t❡ q✉❡ s❡ ♦❜t❡♥❤❛♠ ♥♦✈♦s ♣r♦❝❡ss♦s✱ ❡q✉✐♣❛♠❡♥t♦s✱ ♠ét♦❞♦s ♥♦ ♣r♦❝❡ss♦ ❞❡ tr❛♥s❢♦r♠❛çã♦ ❞❛ ♥❛t✉r❡③❛✱ ❡♥tr❡ ♦✉tr♦s✳ ❆t✉❛❧♠❡♥t❡✱ ❡ss❡ ❝♦♥t❡ú❞♦ é ♠✉✐t♦ ❛❜♦r❞❛❞♦ ♥♦s ❝✉rs♦s s✉♣❡r✐♦r❡s ♥❛s ár❡❛s ❞❡ ❝✐ê♥❝✐❛s ❞❛ ♥❛t✉r❡③❛✱ ❡♥❣❡♥❤❛r✐❛s ❡ t❡❝♥♦❧♦❣✐❛s✳ ❙✉❛ ✐♠♣♦rtâ♥✲ ❝✐❛ s❡ ❞á ♣♦r s✉❛ ❛♣❧✐❝❛❜✐❧✐❞❛❞❡ ❡♠ ❞✐✈❡rs❛s ár❡❛s ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦✳ P♦ré♠ q✉❛♥❞♦ s❡ tr❛t❛ ❞♦ ❡♥s✐♥♦ ❞❡st❡ ❝♦♥t❡ú❞♦ ♥♦ ❡♥s✐♥♦ ♠é❞✐♦ ✐♥❢❡❧✐③♠❡♥t❡ ❡st❡ s❡ t♦r♥❛ ♣♦✉❝♦ ✈❛❧♦r✐③❛❞♦✳ ■♥tr♦❞✉③✐r ❝♦♥❝❡✐t♦s ❞❡ ❈á❧❝✉❧♦ ❉✐❢❡r❡♥❝✐❛❧ ❡ ■♥t❡❣r❛❧ ♥♦ ❊♥s✐♥♦ ▼é❞✐♦ ❛✉①✐❧✐❛ ♥❛ ❝♦♠♣r❡❡♥sã♦ ❞❡ ❛❧❣✉♠❛s ♣r♦♣r✐❡❞❛❞❡s✱ ❡♥tr❡ ❡❧❛s ♦ ❧✐♠✐t❡ ❞❡ ✉♠❛ ❢✉♥çã♦✱ ❢❡rr❛♠❡♥t❛ ✐♥❞✐s♣❡♥sá✈❡❧ ♣❛r❛ ❛ ❝♦♠♣r❡❡♥sã♦ ❞❡ ❢❡♥ô♠❡♥♦s ❢ís✐❝♦s✱ ❝♦♠♦ ✈❡❧♦❝✐❞❛❞❡✱ ❢♦rç❛✱ ❡t❝✳ ❉❡ss❡ ♠♦❞♦✱ ♦ q✉❡ ♣r♦♣♦♠♦s ❛q✉✐ é ❛ ✐♥s❡rçã♦ ❞♦ ❝♦♥t❡ú❞♦ ❞❡ ❝á❧❝✉❧♦ ♥♦ ❊♥s✐♥♦ ▼é❞✐♦✱ q✉❡ ✈❡♠♦s ❝♦♠♦ ✉♠❛ ♦♣çã♦ ✈✐á✈❡❧✱ ❞❡s❞❡ q✉❡ ❛❜♦r❞❛❞❛ ❞❡ ❢♦r♠❛ ❝♦♥t❡①t✉❛❧✐③❛❞❛✳
❆❜str❛❝t
❚❤❡ st✉❞② ♦❢ ❞✐✛❡r❡♥t✐❛❧ ❛♥❞ ■♥t❡❣r❛❧ ❈❛❧❝✉❧✉s ✐s ❝♦♥s✐❞❡r❡❞ ♦♥❡ ♦❢ t❤❡ ♠♦st ✐♥✢✉❡♥t✐❛❧ ♠❛t❤❡♠❛t✐❝❛❧ ❝♦♥t❡♥t ✐♥ ❝✉rr❡♥t s❝✐❡♥t✐✜❝ ❛♥❞ t❡❝❤♥♦❧♦❣✐❝❛❧ ❞❡✈❡❧♦♣♠❡♥t✳ ❆❧❧♦✇s ♦♥❡ t♦ ♦❜t❛✐♥ ♥❡✇ ♣r♦❝❡ss❡s✱ ❡q✉✐♣♠❡♥t✱ ♠❡t❤♦❞s ✐♥ t❤❡ ♣r♦❝❡ss ♦❢ tr❛♥s❢♦r♠❛t✐♦♥ ♦❢ ♥❛t✉r❡✱ ❛♠♦♥❣ ♦t❤❡rs✳ ❈✉rr❡♥t❧②✱ t❤✐s ❝♦♥t❡♥t ✐s ✈❡r② ❞✐s❝✉ss❡❞ ✐♥ ✉♣♣❡r ❝♦✉rs❡s ✐♥ t❤❡ ❛r❡❛s ♦❢ ♥❛t✉r❛❧ s❝✐❡♥❝❡s✱ ❡♥❣✐♥❡❡r✐♥❣ ❛♥❞ t❡❝❤♥♦❧♦❣✐❡s✳ ■ts ✐♠♣♦rt❛♥❝❡ ✐s ❞✉❡ t♦ ✐ts ❛♣♣❧✐❝❛❜✐❧✐t② ✐♥ ❞✐✈❡rs❡ ❛r❡❛s ♦❢ ❦♥♦✇❧❡❞❣❡✳ ❇✉t ✇❤❡♥ ✐t ❝♦♠❡s t♦ t❤❡ t❡❛❝❤✐♥❣ ♦❢ t❤✐s ❝♦♥t❡♥t ✐♥ ❤✐❣❤ s❝❤♦♦❧ ✉♥❢♦rt✉♥❛t❡❧② t❤✐s ❜❡❝♦♠❡s ✉♥❛♣♣r❡❝✐❛t❡❞✳ ■♥tr♦❞✉❝❡ ❝♦♥❝❡♣ts ♦❢ ❞✐✛❡r❡♥t✐❛❧ ❛♥❞ ■♥t❡❣r❛❧ ❈❛❧❝✉❧✉s ✐♥ ❤✐❣❤ s❝❤♦♦❧ ❛ss✐sts ✐♥ ✉♥❞❡rst❛♥❞✐♥❣ ♦❢ s♦♠❡ ♣r♦♣❡rt✐❡s✱ s✉❝❤ ❛s t❤❡ ❧✐♠✐t ♦❢ ❛ ❢✉♥❝t✐♦♥✱ ✐♥❞✐s♣❡♥s❛❜❧❡ t♦♦❧ ❢♦r ✉♥❞❡rst❛♥❞✐♥❣ ♣❤②s✐❝❛❧ ♣❤❡♥♦♠❡♥❛✱ s✉❝❤ ❛s s♣❡❡❞✱ str❡♥❣t❤✱ ❡t❝✳ ❚❤✉s✱ ✇❤❛t ✇❡ ❛r❡ ♣r♦♣♦s✐♥❣ ❤❡r❡ ✐s t❤❡ ✐♥s❡rt✐♦♥ ♦❢ t❤❡ ❝♦♥t❡♥t ♦❢ ❝❛❧❝✉❧✉s ✐♥ ❤✐❣❤ s❝❤♦♦❧ t❤❛t ✇❡ s❡❡ ❛s ❛ ✈✐❛❜❧❡ ♦♣t✐♦♥✱ s✐♥❝❡ ✐t ❞❡❛❧t ✇✐t❤ ❝♦♥t❡①t✉❛❧✐③❡❞ ✇❛②✳
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✷✳✶ ●rá✜❝♦ ❞❛ ❢✉♥çã♦f(x) =x2✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✷ ❈✉r✈❛ ❝✉❥❛ ❝♦♥❝❛✈✐❞❛❞❡ ♥ã♦ é ✈♦❧t❛❞❛ ♣❛r❛ ❝✐♠❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✸ ●rá✜❝♦ ❞❡f(x) =x2 ❡ ❛❧❣✉♠❛s ❞❡ s✉❛s r❡t❛s t❛♥❣❡♥t❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✹ ●rá✜❝♦ ❞❡y=x2✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✷✳✺ ❉✐stâ♥❝✐❛ ❛♣r♦①✐♠❛❞❛ ❡♥tr❡ ❛s r♦❞❛s ❞✐❛♥t❡✐r❛s ❡ tr❛s❡✐r❛s ❞❡ ✉♠ ❝❛rr♦✳ ✷✼
✸✳✶ ●rá✜❝♦ ❞❡ ❛♣r♦①✐♠❛çõ❡s à ❞✐r❡✐t❛ ❡ à ❡sq✉❡r❞❛ ❞❡x= 1♣❛r❛f(x) = 2x+1✳ ✸✼
✸✳✷ ●rá✜❝♦ ❞❡ ❛♣r♦①✐♠❛çõ❡s à ❞✐r❡✐t❛ ❡ à ❡sq✉❡r❞❛ ❞❡ x = 1 ♣❛r❛ f(x) =
x2+x−2
x−1 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽
✸✳✸ ❈♦♠♣♦rt❛♠❡♥t♦ ❞❡f(x)♣❛r❛ ✈❛❧♦r❡s ❞❡ x ♣ró①✐♠♦s ❞❡1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾
✸✳✹ ●rá✜❝♦ ❞❡f(x) =x+ 1, s❡x≤1; f(x) =x+ 3, s❡ x >1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵
✸✳✺ ●rá✜❝♦ ❞❡f(x) =x2✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✸✳✻ ●rá✜❝♦s ❞❡ ❛❧❣✉♠❛s ❢✉♥çõ❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✸✳✼ ●rá✜❝♦ ❞❡ ✉♠❛ ❢✉♥çã♦ ❝✉❥♦ ❧✐♠✐t❡ ❡♠ x= 3 é 0❡ ❡♠ x=−3 ♥ã♦ ❡①✐st❡✳ ✹✷
✸✳✽ ●rá✜❝♦ ❞❛ ❢✉♥çã♦y=√x−1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷
✸✳✾ ●rá✜❝♦ ❞❡g(x) = t❣x✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸
✹✳✶ ❘❡t❛ t❛♥❣❡♥t❡ ❛♦ ❣rá✜❝♦ ❞❡ f ♥♦ ♣♦♥t♦ P✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶
✹✳✷ ❘❡t❛ t❛♥❣❡♥t❡ ❛♦ ❣rá✜❝♦ ❞❡ f ♥♦ ♣♦♥t♦ P✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶
✹✳✸ ❘❡t❛ t❛♥❣❡♥t❡ ❛♦ ❣rá✜❝♦ ❞❡ f ♥✉♠ ♣♦♥t♦ P✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷
✹✳✹ ●rá✜❝♦ ❞❛ ❢✉♥çã♦f(x) =x2✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✹✳✺ ●rá✜❝♦ ❞❡ ✉♠❛ ❢✉♥çã♦f ❡ ✉♠❛ r❡t❛s q✉❡ ♣❛ss❛ ♣❡❧♦s ♣♦♥t♦sA ❡ B✳ ✳ ✺✺
✹✳✻ ●rá✜❝♦s ❞❡ ❛❧❣✉♠❛s ❢✉♥çõ❡s ❝r❡s❝❡♥t❡s ♥♦ ✐♥t❡r✈❛❧♦[0,5]✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻
✹✳✼ ❘❡t❛s t❛♥❣❡♥t❡s ❛ ❞✉❛s ❝✉r✈❛s ❝♦♥✈❡①❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✹✳✽ ❘❡t❛ t❛♥❣❡♥t❡ ❛ ❝✉r✈❛ ♥♦ ♣♦♥t♦P ❡ s❡❝❛♥t❡ ♥♦ ♣♦♥t♦ Q✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽
✹✳✾ ❘❡t❛t t❛♥❣❡♥t❡ à ❝✉r✈❛f1(x) =x3 ♥♦ ♣♦♥t♦ x0 = 0,5✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳✶✵ ❘❡t❛t t❛♥❣❡♥t❡ à ❝✉r✈❛f2(x) =x3−3x2+ 3x+ 1 ♥♦ ♣♦♥t♦ x0 = 1✳ ✳ ✳ ✺✾ ✹✳✶✶ ❘❡t❛t t❛♥❣❡♥t❡ à ❝✉r✈❛f3(x) =x2−4x+ 3 ♥♦ ♣♦♥t♦ x0 = 2✳ ✳ ✳ ✳ ✳ ✳ ✺✾
✹✳✶✷ ❘❡t❛t t❛♥❣❡♥t❡ ❛♦ ❣rá✜❝♦ ❞❡✜♥✐❞♦ ♣♦rf4(x) = x2 −1 ♥♦ ♣♦♥t♦ x0 = 3✳ ✺✾ ✹✳✶✸ ●rá✜❝♦s ❞❡ ❛❧❣✉♠❛s ❢✉♥çõ❡s q✉❡ ♥ã♦ ♣♦ss✉❡♠ ❞❡r✐✈❛❞❛ ❡♠ x0✳ ✭❉❛♥t❡✱
✷✵✵✹❜✱ ♣✳ ✷✻✹✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✹✳✶✹ ●rá✜❝♦ ❞❡ ✉♠❛ ❢✉♥çã♦ ♥ã♦✲❞❡r✐✈á✈❡❧ ❡♠ x0✳ ✭❉❛♥t❡✱ ✷✵✵✹❜✱ ♣✳ ✷✮ ✳ ✳ ✳ ✻✹ ✹✳✶✺ ●rá✜❝♦ ❞❡ ✉♠❛ ❢✉♥çã♦ ❡♠ q✉❡ ♥ã♦ ❡①✐st❡ ❞❡r✐✈❛❞❛ ❡♠ x0✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹
✺✳✶ ➪r❡❛ s♦❜ ♦ ❣rá✜❝♦ ❞❡ f✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺
✺✳✷ ❙♦♠❛ ❞❡ ❘✐❡♠❛♥♥ ❡♠ [a, b]❞❡ ✉♠❛ ❢✉♥çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸
✺✳✸ ❆♣r♦①✐♠❛çã♦ ❞❛ ár❡❛ s♦❜ ❛ ❝✉r✈❛ y(x) =√1−x2 ♥♦ ✐♥t❡r✈❛❧♦ [0,1]♣♦r ✷ r❡tâ♥❣✉❧♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✺✳✹ ❆♣r♦①✐♠❛çã♦ ❞❛ ár❡❛ s♦❜ ❛ ❝✉r✈❛ y(x) =√1−x2 ♥♦ ✐♥t❡r✈❛❧♦ [0,1]♣♦r
✹ r❡tâ♥❣✉❧♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✺✳✺ ❆♣r♦①✐♠❛çã♦ ❞❛ ár❡❛ s♦❜ ❛ ❝✉r✈❛ y(x) =√1−x2 ♥♦ ✐♥t❡r✈❛❧♦ [0,1]♣♦r
✽ r❡tâ♥❣✉❧♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽ ✺✳✻ ●rá✜❝♦ ❞❡ ✉♠❛ ❢✉♥çã♦ ❝♦♥st❛♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✺✳✼ ●rá✜❝♦ ❞❡ ✉♠❛ ❢✉♥çã♦ ❧✐♥❡❛r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾
✻✳✶ ❮♥❞✐❝❡ ❞❡ ❛♣r♦✈❛çã♦ ♥❛ ❞✐s❝✐♣❧✐♥❛ ❋✉♥❞❛♠❡♥t♦s ❞❡ ▼❛t❡♠át✐❝❛✱ ♣❡rí♦❞♦ ✷✵✶✷✴✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼ ✻✳✷ ❮♥❞✐❝❡ ❞❡ ❛♣r♦✈❛çã♦ ♥❛ ❞✐s❝✐♣❧✐♥❛ ❈á❧❝✉❧♦ ■✱ ♣❡rí♦❞♦ ✷✵✶✷✴✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼ ✻✳✸ ❮♥❞✐❝❡ ❞❡ ❛♣r♦✈❛çã♦ ♥❛ ❞✐s❝✐♣❧✐♥❛ ❈á❧❝✉❧♦ ■■✱ ♣❡rí♦❞♦ ✷✵✶✷✴✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✻✳✹ ❮♥❞✐❝❡ ❞❡ ❛♣r♦✈❛çã♦ ♥❛ ❞✐s❝✐♣❧✐♥❛ ❋✉♥❞❛♠❡♥t♦s ❞❡ ▼❛t❡♠át✐❝❛✱ ♣❡rí♦❞♦
✷✵✶✸✴✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✻✳✺ ❮♥❞✐❝❡ ❞❡ ❛♣r♦✈❛çã♦ ♥❛ ❞✐s❝✐♣❧✐♥❛ ❈á❧❝✉❧♦ ■✱ ♣❡rí♦❞♦ ✷✵✶✸✴✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✻✳✻ ❮♥❞✐❝❡ ❞❡ ❛♣r♦✈❛çã♦ ♥❛ ❞✐s❝✐♣❧✐♥❛ ❈á❧❝✉❧♦ ■■✱ ♣❡rí♦❞♦ ✷✵✶✸✴✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✻✳✼ ❋✉♥❞❛♠❡♥t♦s ❞❡ ▼❛t❡♠át✐❝❛ ✲ ❝♦♠♣❛r❛çõ❡s ❞♦s ♥ã♦ ❛♣r♦✈❛❞♦s ❞♦s ❛♥♦s
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✷✳✶ ❱❛❧♦r❡s q✉❡ ❡✈✐❞❡♥❝✐❛♠ ❛ s✐♠❡tr✐❛ ❞♦ ❣rá✜❝♦ ❞❛ ❢✉♥çã♦f(x) = x2✳ ✳ ✳ ✳ ✷✹ ✸✳✶ ◗✉❛❞r♦ ❞❡ s✉❝❡ssõ❡s ♥✉♠ér✐❝❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✸✳✷ ❆♣r♦①✐♠❛çã♦ à ❞✐r❡✐t❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✸✳✸ ❆♣r♦①✐♠❛çã♦ à ❡sq✉❡r❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✸✳✹ ❆♣r♦①✐♠❛çã♦ à ❞✐r❡✐t❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✸✳✺ ❆♣r♦①✐♠❛çã♦ à ❡sq✉❡r❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✸✳✻ ❈♦♠♣♦rt❛♠❡♥t♦ ❞❡ f(x) = x+ 3 ♣❛r❛ ✈❛❧♦r❡s ❞❡ x ♣ró①✐♠♦s ❞❡ 1 ♣❡❧❛
❡sq✉❡r❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✸✳✼ ❈♦♠♣♦rt❛♠❡♥t♦ ❞❡ f(x) = x+ 3 ♣❛r❛ ✈❛❧♦r❡s ❞❡ x ♣ró①✐♠♦s ❞❡ 1 ♣❡❧❛
❞✐r❡✐t❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✸✳✽ ❈♦♠♣♦rt❛♠❡♥t♦ ❞❡ f(x) = x2 ♣❛r❛ ✈❛❧♦r❡s ❞❡ x ♣ró①✐♠♦s ❞❡ 2 ❡ ♣❛r❛
x= 2✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵
✸✳✾ ❈♦♠♣♦rt❛♠❡♥t♦ ❞❡ y = √x−1 ♣❛r❛ ✈❛❧♦r❡s ❞❡ x ♣ró①✐♠♦s ❞❡ 1 ♣❡❧❛
❞✐r❡✐t❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✸✳✶✵ ❈♦♠♣♦rt❛♠❡♥t♦ ❞❡y =√x−1 ♣❛r❛ xs✉✜❝✐❡♥t❡♠❡♥t❡ ❣r❛♥❞❡✳ ✳ ✳ ✳ ✳ ✳ ✹✸
✹✳✶ ❱❛r✐❛çã♦ ❞❡ três ❢✉♥çõ❡s ❝r❡s❝❡♥t❡s ♥♦ ✐♥t❡r✈❛❧♦[0,5]✭❙▼❖▲❊ ✫ ❉■◆■❩✱
✷✵✵✸✱ ♣✳ ✷✼✽✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻
❙✉♠ár✐♦
■◆❚❘❖❉❯➬➹❖ ✶✷
✶ ➱ P❖❙❙❮❱❊▲ ❊❙❚❯❉❆❘ ❈➪▲❈❯▲❖ ◆❖ ❊◆❙■◆❖ ▼➱❉■❖❄ ✶✺
✷ ❋❯◆➬➹❖✿ P❘➱✲❘❊◗❯■❙■❚❖ ❋❯◆❉❆▼❊◆❚❆▲ P❆❘❆ ❖ ❊❙❚❯❉❖
❉❖ ❈➪▲❈❯▲❖ ✷✵
✷✳✶ ❊✈♦❧✉çã♦ ❤✐stór✐❝❛ ❞♦ ❝♦♥❝❡✐t♦ ❞❡ ❢✉♥çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✷✳✷ ❆♣r♦①✐♠❛çõ❡s q✉❡ ♣♦❞❡♠ s❡r ✉s❛❞❛s ♥♦ ❡♥s✐♥♦ ♠é❞✐♦ ♣❛r❛ ✐♥tr♦❞✉③✐r ❛
✐❞❡✐❛ ❞❡ ❧✐♠✐t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹
✸ ❋❆▲❆◆❉❖ ❙❖❇❘❊ ▲■▼■❚❊❙ ✸✵
✸✳✶ ❍✐stór✐❛ ❞♦s ❧✐♠✐t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✸✳✷ ◆♦çã♦ ✐♥t✉✐t✐✈❛ ❞❡ ❧✐♠✐t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✸✳✷✳✶ ❉❡✜♥✐çã♦ ✐♥❢♦r♠❛❧ ❞❡ ❧✐♠✐t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✸✳✸ ▲✐♠✐t❡s ❧❛t❡r❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽
✹ ❉❊❘■❱❆❉❆ ✹✺
✹✳✶ ❍✐stór✐❛ ❞❛ ❞❡r✐✈❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✹✳✷ ❆ ❍✐stór✐❛ ❞❛ ❞❡r✐✈❛❞❛ ❞❡ ▼❛r✐❛♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✹✳✸ ❋❛❧❛♥❞♦ s♦❜r❡ ❞❡r✐✈❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✹✳✸✳✶ ❆ r❡t❛ t❛♥❣❡♥t❡ ❛ ✉♠ ❣rá✜❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✹✳✸✳✷ ❆ t❛①❛ ❞❡ ✈❛r✐❛çã♦ ✐♥st❛♥tâ♥❡❛ ❡ s✉❛ ✐♥t❡r♣r❡t❛çã♦ ❣❡♦♠étr✐❝❛ ✳ ✻✵ ✹✳✸✳✸ ❊①♣r❡ss❛♥❞♦ ❛❧❣❡❜r✐❝❛♠❡♥t❡ ❛ t❛①❛ ❞❡ ✈❛r✐❛çã♦ ✐♥st❛♥tâ♥❡❛ ✳ ✳ ✳ ✻✶ ✹✳✹ ❆ ❞❡r✐✈❛❞❛ ❡♠ ✉♠ ♣♦♥t♦ ❡ ❛ ❢✉♥çã♦ ❞❡r✐✈❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸
✺ ■◆❚❊●❘❆▲ ✻✺
✺✳✶ ❍✐stór✐❛ ❞❛ ■♥t❡❣r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✺✳✷ ❆ ■♥t❡❣r❛❧ ❞❡ ❘✐❡♠❛♥♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✺✳✸ ◆♦çã♦ ■♥t✉✐t✐✈❛ ❞❡ ■♥t❡❣r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹
✺✳✸✳✶ ❖ ♠ét♦❞♦ ❞❛ ❡①❛✉stã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✺✳✹ ➪r❡❛ s♦❜ ❢✉♥çõ❡s s✐♠♣❧❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾
✻ ❈➪▲❈❯▲❖ ◆❖ ❊◆❙■◆❖ ❙❯P❊❘■❖❘ ✽✶
✻✳✶ P❛r❛ q✉❡ ❙❡r✈❡ ♦ ❈á❧❝✉❧♦ ❉✐❢❡r❡♥❝✐❛❧ ❡ ■♥t❡❣r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✻✳✷ ❘❡♣r♦✈❛çõ❡s ♥❛ ❞✐s❝✐♣❧✐♥❛ ❞❡ ❈á❧❝✉❧♦ ❉✐❢❡r❡♥❝✐❛❧ ❡ ■♥t❡❣r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸
❈❖◆❙■❉❊❘❆➬Õ❊❙ ❋■◆❆■❙ ✾✷
■◆❚❘❖❉❯➬➹❖
◆ã♦ s❡ ♣♦❞❡ ♥❡❣❛r ❛ ✐♠♣♦rtâ♥❝✐❛ ❞❛ ♠❛t❡♠át✐❝❛ ♣❛r❛ ♦ ❤♦♠❡♠ ♠♦❞❡r♥♦✱ ♣♦r ✐ss♦ ♦ s❡✉ ❡♥s✐♥♦ ❞❡✈❡ s❡r ♦❜❥❡t♦ ❞❡ ❡st✉❞♦ ❞❛ ❝✐ê♥❝✐❛✱ t❡♥❞♦ ❝♦♠♦ ❜❛s❡ ♣r✐♥❝✐♣❛❧ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ s❡ ❝♦♥str✉✐r✱ r❡❝♦♥str✉✐r ❡ ♣❡r♣❡t✉❛r ♦s ❝♦♥❤❡❝✐♠❡♥t♦s ♣r♦❞✉③✐❞♦s ♣♦r ❡❧❛✱ ❡ tê♠ ❝♦♠♦ ❢✉♥çã♦ s♦❝✐❛❧ ❝❛♣❛❝✐t❛r ✐♥❞✐✈í❞✉♦s ♣❛r❛ r❡s♦❧✈❡r❡♠ ♣r♦❜❧❡♠❛s✳
❖ ♠✉♥❞♦ ❛t✉❛❧ ♥❡❝❡ss✐t❛ ❞❡ ✉♠❛ ♠✉❞❛♥ç❛ ♥❛ ❢♦r♠❛ ❞❡ s❡ ❝♦♥❝❡❜❡r ♦ ❡♥s✐♥♦ ❞❛ ♠❛t❡♠át✐❝❛ ♥♦s ❞✐✈❡rs♦s ♥í✈❡✐s✱ s❡♥❞♦ ❡❧❡ ❢✉♥❞❛♠❡♥t❛❧✱ ♠é❞✐♦✱ ♦✉ s✉♣❡r✐♦r✱ ✐ss♦ ❞❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❡ q✉❡ ❝♦♠ ❛ ❣❧♦❜❛❧✐③❛çã♦ ♦ ❡♥s✐♥♦ ❡♥❝✐❝❧♦♣é❞✐❝♦✱ ♦♥❞❡ ♦ ❛❧✉♥♦ ❛♣❡♥❛s r❡❝❡❜❡ ❝♦♥❤❡❝✐♠❡♥t♦ ❡ ♥ã♦ s❡ ♣♦s✐❝✐♦♥❛ ❝r✐t✐❝❛♠❡♥t❡ ❢r❡♥t❡ ❛ ❡❧❡✱ ♥ã♦ ❢❛③ ♠❛✐s s❡♥t✐❞♦✳ ■ss♦ ♣♦rq✉❡ ❛s ❣r❛♥❞❡s ♠✉❞❛♥ç❛s q✉❡ ✈❡♠ ♦❝♦rr❡♥❞♦✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❛ ♣❛rt✐r ❞♦ ✜♥❛❧ ❞♦ sé❝✉❧♦ ♣❛ss❛❞♦✱ tê♠ ❣❡r❛❞♦ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ s❡ ♣❡♥s❛r ♥❛ ✈✐❞❛ ❞♦ ❤♦♠❡♠ ♠♦❞❡r♥♦✱ s♦❜r❡t✉❞♦ ♥♦ q✉❡ ❞✐③ r❡s♣❡✐t♦ à ❡❞✉❝❛çã♦✳
❚❡♠♦s ♦ ❝á❧❝✉❧♦ ❝♦♠♦ ✉♠❛ ❞❛s ❣r❛♥❞❡s ❢❡rr❛♠❡♥t❛s ❞❛ ♠❛t❡♠át✐❝❛✱ ❛♦♥❞❡ ✈❡♠ s❡♥❞♦ ❞❡s❡♥✈♦❧✈✐❞♦ ❞❡s❞❡ ❆rq✉✐♠❡❞❡s ❛té ❝❤❡❣❛r❡♠ ❛ ◆❡✇t♦♥ ❡ ▲❡✐❜♥✐③✱ ❞❛❞❛ t❛♠❛♥❤❛ ✐♠♣♦rtâ♥❝✐❛ ❞❡✈❡♠♦s tr❛t❛r ❞❛ ❝♦♥✈❡♥✐ê♥❝✐❛ ❞❡ ✐♥❝❧✉í✲❧♦ ♥♦ ❡♥s✐♥♦ ♠é❞✐♦✱ ❞❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❡ s✉❛ r❡❧❡✈â♥❝✐❛ ♥❛ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s✳
❊♠❜♦r❛ ❣r❛♥❞❡ ♣❛rt❡ ❞♦s ❧✐✈r♦s ❞❡ ❡♥s✐♥♦ ♠é❞✐♦ ✐♥❝❧✉✐ ♦ ❝á❧❝✉❧♦ ❡♥tr❡ s❡✉s tó♣✐❝♦s✱ ❛✐♥❞❛ sã♦ ♠✉✐t♦ ♣♦✉❝♦ ❡♥s✐♥❛❞♦s ❡ ❡♥t❡♥❞❡♠♦s q✉❡ ❞❡s❝❛rt❛r ♦ ❝á❧❝✉❧♦ ♥♦ ❡♥s✐♥♦ ♠é❞✐♦ é ❣r❛✈❡✱ ♣♦✐s ❡st❛♠♦s ❞❡✐①❛♥❞♦ ❞❡ ❧❛❞♦ ✉♠❛ ❝♦♠♣♦♥❡♥t❡ r❡❧❡✈❛♥t❡ ♣❛r❛ ❛ ❢♦r♠❛çã♦ ❞♦ ❛❧✉♥♦ ♥♦ ❝♦♥t❡①t♦ ❞❡ ❡♥s✐♥♦ ❛t✉❛❧✱ q✉❡ ❝♦♥tr✐❜✉✐ ❞❡ ♠❛♥❡✐r❛ ❡①♣r❡ss✐✈❛ ♣❛r❛ ♦ r❡s❣❛t❡ ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦ ♥♦ ❝❛♠♣♦ ❞❛ ♠❛t❡♠át✐❝❛ ❡ s✉❛s r❛♠✐✜❝❛çõ❡s✳
❆ ▲❡✐ ❞❡ ❉✐r❡tr✐③❡s ❡ ❇❛s❡s ✭▲❉❇✮ ❡♠ s❡✉ ❛rt✐❣♦ ✷✷ ❞✐③✿ ✏❆ ❡❞✉❝❛çã♦ ❜ás✐❝❛ t❡♠ ♣♦r ✜♥❛❧✐❞❛❞❡ ❞❡s❡♥✈♦❧✈❡r ♦ ❡❞✉❝❛♥❞♦✱ ❛ss❡❣✉r❛r✲❧❤❡ ❛ ❢♦r♠❛çã♦ ❝♦♠✉♠ ✐♥❞✐s♣❡♥sá✈❡❧ ♣❛r❛ ♦ ❡①❡r❝í❝✐♦ ❞❛ ❝✐❞❛❞❛♥✐❛ ❡ ❢♦r♥❡❝❡✲❧❤❡s ♠❡✐♦s ♣❛r❛ ♣r♦❣r❡❞✐r ♥♦ tr❛❜❛❧❤♦ ❡ ❡♠ ❡st✉❞♦s ♣♦st❡r✐♦r❡s✳✑
✶✸
❛s ♥♦✈❛s s✐♠❜♦❧♦❣✐❛s✱ ❛té ♣♦rq✉❡ ❣r❛♥❞❡ ♣❛rt❡ ❞❡❧❡s ✐rá ❡st✉❞❛r ❛❧❣✉♠❛ ❞✐s❝✐♣❧✐♥❛ ❞❡ ❝á❧❝✉❧♦ ♥♦ ♥í✈❡❧ s✉♣❡r✐♦r✳
➱ ✐♠♣♦rt❛♥t❡ s❛❧✐❡♥t❛r q✉❡ ✐♥s❡r✐r ♦ ❝á❧❝✉❧♦ ♥♦ ❡♥s✐♥♦ ♠é❞✐♦ ♥ã♦ é t❛r❡❢❛ ❢á❝✐❧✱ ✐ss♦ ♣♦rq✉❡ ♦ ❡♥t❡♥❞✐♠❡♥t♦ ❞❡ ♥♦✈❛s s✐♠❜♦❧♦❣✐❛s é ❝♦♠♣❧✐❝❛❞♦ ♣❛r❛ ❜♦❛ ♣❛rt❡ ❞♦s ❛❧✉♥♦s✳ P❛r❛ ▲♦♣❡s ✭❛♣✉❞ ▼❆❈❍❆❉❖✱ ✷✵✵✷✱ ♣✳ ✶✹✮✿
❬✳✳✳❪ ❡♠ t♦❞♦s ♦s ♣❛ís❡s✱ ❡❞✉❝❛❞♦r❡s ❡ ♠❛t❡♠át✐❝♦s ❜✉s❝❛♠ ❡♥❝♦♥tr❛r ♠ét♦❞♦s q✉❡ ✈✐s❡♠ ❢❛❝✐❧✐t❛r ♦ ❡♥t❡♥❞✐♠❡♥t♦ ❞♦ ❈á❧❝✉❧♦ ♣♦r ♣❛rt❡ ❞♦s ❡st✉❞❛♥t❡s✳ ▼✉✐t♦ t❡♠ s❡ ❝♦♥s❡❣✉✐❞♦✱ ♠❛s é ✐♠♣♦rt❛♥t❡ ❞✐③❡r q✉❡ ♥❡♥❤✉♠❛ ❢ór♠✉❧❛ ♠á❣✐❝❛ ❢♦✐ ❡♥❝♦♥tr❛❞❛ ❛té ❤♦❥❡ ✭▲❖P❊❙ ❛♣✉❞ ▼❆❈❍❆❉❖✱ ✷✵✵✷✱ ♣✳ ✶✹✮✳
❉❡✈❡✲s❡ ❡♥tã♦ ❤❛✈❡r ✉♠❛ ♣r♦♣♦st❛ ❞❡ ✐♥❝❡♥t✐✈♦ ❛♦s ❛❧✉♥♦s✱ ♣r♦❝✉r❛♥❞♦ ♠ét♦❞♦s q✉❡ ❢❛❝✐❧✐t❡♠ ♦ ❡♥t❡♥❞✐♠❡♥t♦ ❞❛ ❞✐s❝✐♣❧✐♥❛✱ q✉❡ s❡ ❛♣r❡s❡♥t❛❞❛ ❝♦♥✈❡♥✐❡♥t❡♠❡♥t❡ ♣♦❞❡ s❡r ❣r❛t✐✜❝❛♥t❡✱ ❤❛❥❛ ✈✐st♦ ❛s ✐♥t❡r❡ss❛♥t❡s ❛♣❧✐❝❛çõ❡s ❞❛ ❞❡r✐✈❛❞❛ ❡♠ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s✱ t❛✐s ❝♦♠♦ ♠á①✐♠♦s ❡ ♠í♥✐♠♦s✱ ❞❛ ❢✉♥çã♦ ❡①♣♦♥❡♥❝✐❛❧ ❝♦♠ ♣r♦❜❧❡♠❛s ❞❡ ❝r❡s❝✐♠❡♥t♦ ❞❡ ♣♦♣✉❧❛çõ❡s✱ ❡♥tr❡ ♦✉tr♦s✳
❆❝r❡❞✐t❛✲s❡ q✉❡ ✐♥s❡r✐♥❞♦ ♦ ❝á❧❝✉❧♦ ♥♦ ❡♥s✐♥♦ ♠é❞✐♦✱ ❢❛③❡♥❞♦ ❝♦♠ q✉❡ ♦ ❛❧✉♥♦ ❡♥tr❡ ❡♠ ❝♦♥t❛t♦ ❝♦♠ ❛ ❞✐s❝✐♣❧✐♥❛ ♠❛✐s ❝❡❞♦✱ ❞✐♠✐♥✉✐r✐❛ ❛ ❣r❛♥❞❡ t❛①❛ ❞❡ ❡✈❛sã♦ ❞♦s ❝✉rs♦s s✉♣❡r✐♦r❡s q✉❡ t❡♠ ❝♦♠♦ ❜❛s❡ ❢✉♥❞❛♠❡♥t❛❧ ♦ ❝á❧❝✉❧♦✳ P❛r❛ ❇❛rr❡t♦ ✭❛♣✉❞ ❘❊■❙✱ ✷✵✵✺✱ ♣✳ ✹✮✿
❖ ❡♥s✐♥♦ ❞❡ ❈á❧❝✉❧♦ ♥❛s ✉♥✐✈❡rs✐❞❛❞❡s ❜r❛s✐❧❡✐r❛s t❡♠ s✐❞♦ ♦❜❥❡t♦ ❞❡ q✉❡st✐♦♥❛♠❡♥t♦ ❡♠ ❞✐✈❡rs♦s ❢ór✉♥s ❡♠ ❢✉♥çã♦ ❞❛s ❞✐✜❝✉❧❞❛❞❡s ❛♣r❡s❡♥t❛❞❛s ♣❡❧♦s ❛❧✉♥♦s ♥❛ s✉❛ ❛♣r❡♥❞✐③❛❣❡♠✱ ❜❡♠ ❝♦♠♦ ♣❡❧❛ ❛❧t❛ ❡✈❛sã♦ ❞♦s ❡st✉❞❛♥t❡s ❞♦s ♣r✐♠❡✐r♦s ♣❡rí♦❞♦s✱ ♠❛tr✐❝✉❧❛❞♦s ♥❡st❛ ❞✐s✲ ❝✐♣❧✐♥❛ ✭❇❆❘❘❊❚❖ ❛♣✉❞ ❘❊■❙✱ ✷✵✵✺✱ ♣✳ ✹✮✳
❙❛❜❡✲s❡ q✉❡ ♦ ❝á❧❝✉❧♦ é ❞❡ ❢✉♥❞❛♠❡♥t❛❧ ✐♠♣♦rtâ♥❝✐❛ ♣❛r❛ ♦s ❝✉rs♦s ❞❡ ♠❛t❡♠á✲ t✐❝❛✱ ❡♥❣❡♥❤❛r✐❛✱ ❢ís✐❝❛✱ ❝✐ê♥❝✐❛s ❞❛ ❝♦♠♣✉t❛çã♦✱ ❡♥tr❡ ♦✉tr♦s✳ ❙❡♥❞♦ ❛ss✐♠✱ ❞❡✈❡♠♦s ❧❡✈á✲❧♦ ♠❛✐s ❛ sér✐♦ ♣♦rq✉❡ ❡ss❡s ❛❧✉♥♦s ❡♥tr❛♠ ♥❛s ✉♥✐✈❡rs✐❞❛❞❡s s❡♠ ❡st❛r ❞❡✈✐❞❛✲ ♠❡♥t❡ ♣r❡♣❛r❛❞♦s✱ ❝❛✉s❛♥❞♦ ❡♥tã♦ ✉♠ í♥❞✐❝❡ ❛❧❛r♠❛♥t❡ ❞❡ ❞❡s✐stê♥❝✐❛s ❡ r❡♣r♦✈❛çõ❡s✳ ❊♠ s✉❛s ♣❡sq✉✐s❛s✱ ❇❛r✉✜ ✭✶✾✾✺✴✶✾✾✾✮ ❞❡st❛❝❛ ♦s ❛❧t♦s í♥❞✐❝❡s ❞❡ ♥ã♦✲❛♣r♦✈❛çã♦ ✭❛❧✉♥♦s r❡♣r♦✈❛❞♦s ♣♦r ♥♦t❛✱ ❢❛❧t❛ ♦✉ ❞❡s✐stê♥❝✐❛✮ ♥❛ ❞✐s❝✐♣❧✐♥❛✱ ❝❤❡❣❛♥❞♦ ❛ ✉♠ ♣❡r✲ ❝❡♥t✉❛❧ ❛❧❛r♠❛♥t❡ ❞❡66,9%✳ P♦r ✐ss♦ ❞❡❢❡♥❞❡♠♦s ❛ ✐❞❡✐❛ ❞❡ ❢❛♠✐❧✐❛r✐③❛r ♦ ❛❧✉♥♦ ❥á ♥♦s
♣r✐♠❡✐r♦s ❛♥♦s ❞♦ ❡♥s✐♥♦ ♠é❞✐♦✱ ♣❛r❛ q✉❡ ♥ã♦ ❤❛❥❛ ✉♠ ❝❤♦q✉❡ ❛♦ ❞❡♣❛r❛r ❝♦♠ ❡❧❛ ♥♦ ♥í✈❡❧ s✉♣❡r✐♦r✳
✶✹
✉♠ ❡①❛❣❡r♦✳ ◆❡ss❡ s❡♥t✐❞♦✱ ♦ ♣r♦❢❡ss♦r ❞❡✈❡r✐❛ ✐♥✐❝✐❛r ♦ ❡♥s✐♥♦ ♠é❞✐♦ r❡t♦♠❛♥❞♦ r❡❣r❛ ❞❡ três ❡ ♣r♦♣♦r❝✐♦♥❛❧✐❞❛❞❡✱ ❞❛í ❡♥tã♦ s✉r❣✐r à ✐❞❡✐❛ ❞❛ ❡q✉❛çã♦ ❞❛ r❡t❛ y = mx+n✱
♣♦❞❡♥❞♦ ♥❡ss❡ ♠♦♠❡♥t♦ ❢❛❧❛r ❞❡ ❛❝rés❝✐♠♦s ❡ ❞❡❝rés❝✐♠♦s✱ ❢❛♠✐❧✐❛r✐③❛♥❞♦ ♦ ❛❧✉♥♦ ❝♦♠ ❛ ♥♦t❛çã♦∆x✭❞❡❧t❛x✮ ❡ ∆y ✭❞❡❧t❛y✮✱ ❡ ❝♦♠ ♦ ❢❛t♦ ❞❡ q✉❡ ♦ ❞❡❝❧✐✈❡ ❞❛ r❡t❛ é ∆y/∆x✳
❙♦❜ ❡ss❡ ♣♦♥t♦ ❞❡ ✈✐st❛✱ ❡♥t❡♥❞❡♠♦s q✉❡ ❛ ✐❞❡✐❛ ✐♥t✉✐t✐✈❛ ❞❡ ❧✐♠✐t❡ ❡ ❞❡r✐✈❛❞❛ ♣♦❞❡♠ s❡r ❞✐s❝✉t✐❞❛s s❡♠ ♠✉✐t♦s r❡❝❡✐♦s ♥♦ ❡♥s✐♥♦ ♠é❞✐♦✳ P♦❞❡♠♦s ❝♦♠❡ç❛r✱ ♣♦r ❡①❡♠✲ ♣❧♦✱ r❡❧❛❝✐♦♥❛♥❞♦ ❡ss❛s ✐❞❡✐❛s ❝♦♠ ♣r♦❜❧❡♠❛s ❝♦t✐❞✐❛♥♦s ❞❡ ♥♦ss❛ s♦❝✐❡❞❛❞❡✳ ◗✉❛♥❞♦ s❡ ❢❛❧❛ ❞❡ ❧✐♠✐t❡✱ ✉♠❛ ❣r❛♥❞❡ ❞✐✜❝✉❧❞❛❞❡ ❡♥❝♦♥tr❛❞❛ ♣❡❧♦ ♣r♦❢❡ss♦r é ♠♦str❛r q✉❡ q✉❛♥❞♦ ❢❛③❡♠♦s ✉♠ x t❡♥❞❡r ✭s❡ ❛♣r♦①✐♠❛r✮ ❞❡ ✉♠ x0✱ ❡❧❡ ♥✉♥❝❛✱ ❞❡ ❢❛t♦✱ ❛❧❝❛♥ç❛rá ❡ss❡ x0✳ ■st♦✱ ❛♣❛r❡♥t❡♠❡♥t❡✱ ♥♦s ♣❛r❡❝❡ ✉♠ ❝♦♥tr❛✲s❡♥s♦ ❝♦♠ ❛ ♥♦ss❛ ✐❞❡✐❛ ❞❡ ❞✐stâ♥❝✐❛✳
P♦❞❡♠♦s✱ ❡♥tã♦✱ ❢❛③❡r ✉♠❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❢❛❧❛♥❞♦ ❞❛ ✜s❝❛❧✐③❛çã♦ ❡❧❡trô♥✐❝❛ ❞❡ ✈❡❧♦❝✐❞❛❞❡ ✭r❛❞❛r❡s✮✱ q✉❡ ❡stã♦ ❡s♣❛❧❤❛❞♦s ❡♠ ❣r❛♥❞❡ ♣❛rt❡ ❞❛s ❝✐❞❛❞❡s ❜r❛s✐❧❡✐✲ r❛s✱ ❡ ❢❛❧❛r ❞❛ ✈❡❧♦❝✐❞❛❞❡ ✐♥st❛♥tâ♥❡❛ ❞❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ✈❡í❝✉❧♦✱ ❞✐③❡♥❞♦ q✉❡ ♦ q✉❡ ❡stá s❡♥❞♦ ❝❛❧❝✉❧❛❞♦✱ ♥❛ ✈❡r❞❛❞❡✱ é ❛ ✈❡❧♦❝✐❞❛❞❡ ♠é❞✐❛ ♥✉♠ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦ ❜❡♠ ♣❡q✉❡♥♦✳ ❊ ❞❡♣❡♥❞❡♥❞♦ ❞❛ ♣r❡❝✐sã♦ ❞♦ ❡q✉✐♣❛♠❡♥t♦✱ q✉❛♥t♦ ♠❡♥♦r s❡ ❝♦♥s❡❣✉✐r ❡ss❡ t❡♠♣♦✱ ♠❡❧❤♦r ❛ ❛♣r♦①✐♠❛çã♦✳
❊ ❝♦♠♦ ♥❡ss❡ ❝❛s♦ ♥ã♦ ✈❛♠♦s t❡r ✉♠❛ ✈❛r✐á✈❡❧ ❞❡ t❡♠♣♦ ③❡r♦✱ ❛ ✐❞❡✐❛ é ❢❛③❡r ❡ss❛ ✈❛r✐❛çã♦ t❡♥❞❡r ❛ ③❡r♦✳ ❯s❛♥❞♦ ❡ss❛ s✐♠♣❧❡s ✐❞❡✐❛✱ ♣♦❞❡♠♦s✱ ❡♥tã♦✱ ✐♥tr♦❞✉③✐r ❛ ✐❞❡✐❛ ❞❡ ❧✐♠✐t❡ ❡ ❞❡r✐✈❛❞❛ ♣❛r❛ ❛❧✉♥♦s ❞♦ ❡♥s✐♥♦ ♠é❞✐♦✳
Cap´ıtulo
1
➱ P❖❙❙❮❱❊▲ ❊❙❚❯❉❆❘ ❈➪▲❈❯▲❖ ◆❖
❊◆❙■◆❖ ▼➱❉■❖❄
❙❡r✐❛ ♠✉✐t♦ ♠❛✐s ♣r♦✈❡✐t♦s♦ q✉❡ t♦❞♦ ♦ t❡♠♣♦ q✉❡ ❤♦❥❡ s❡ ❣❛st❛✱ ♥♦ ✷◦
❣r❛✉✱ ❡♥s✐♥❛♥❞♦ ❢♦r♠❛❧✐s♠♦ ❡ ❧♦♥❣❛ t❡r♠✐♥♦❧♦❣✐❛ s♦❜r❡ ❢✉♥çõ❡s✱ q✉❡ t♦❞♦ ❡ss❡ t❡♠♣♦ ❢♦ss❡ ✉t✐❧✐③❛❞♦ ❝♦♠ ♦ ❡♥s✐♥♦ ❞❛s ♥♦çõ❡s ❜ás✐❝❛s ❞♦ ❈á❧❝✉❧♦ ❡ s✉❛s ❛♣❧✐❝❛çõ❡s✳ ❊♥tã♦✱ ❛♦ ❧♦♥❣♦ ❞❡ss❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦✱ ♦ ❡♥s✐♥♦ ❞❛s ❢✉♥çõ❡s s❡r✐❛ ❢❡✐t♦ ♥♦ ❝♦♥t❡①t♦ ❛♣r♦♣r✐❛❞♦✱ ❞❡ ♠❛♥❡✐r❛ ❡s♣♦♥tâ♥❡❛✱ ♣r♦❣r❡ss✐✈❛ ❡ ♣r♦✈❡✐t♦s❛✳ ✭➪❱■▲❆✱ ✶✾✾✶✱ ♣✳ ✺✮
❖ ❡♥s✐♥♦✲❛♣r❡♥❞✐③❛❣❡♠ ❡♠ ♠❛t❡♠át✐❝❛ t❡♠ s✐❞♦ ♠♦t✐✈♦ ❞❡ ❞✐✈❡rs❛s ❞✐s❝✉ssõ❡s✱ ❞❡s❞❡ ♦ ❡♥s✐♥♦ ❢✉♥❞❛♠❡♥t❛❧ ❛♦ ❡♥s✐♥♦ s✉♣❡r✐♦r✳ ●r❛♥❞❡ ♣❛rt❡ ❞♦s ❛❧✉♥♦s ❢r❡q✉❡♥t❡✲ ♠❡♥t❡ ❞❡♠♦♥str❛ ❞✐✜❝✉❧❞❛❞❡s ♥❛ ❝♦♠♣r❡❡♥sã♦ ❞♦s ❝♦♥❝❡✐t♦s ♠❛t❡♠át✐❝♦s ❢✉♥❞❛♠❡♥✲ t❛✐s✳ ▼✉✐t♦s ❞❡❧❡s ♥ã♦ ❡♥❝♦♥tr❛♠ s❡♥t✐❞♦ ♦✉ ❛♣❧✐❝❛çã♦ ❞♦s ❝♦♥t❡ú❞♦s ❛❜♦r❞❛❞♦s ❡♠ s❛❧❛ ❞❡ ❛✉❧❛✳ ❊ss❛s ❞✐✜❝✉❧❞❛❞❡s ♥ã♦ s❡ ❧✐♠✐t❛♠ ❛♣❡♥❛s ❛♦s ❝♦♥❝❡✐t♦s ❜ás✐❝♦s✱ ✉♠❛ ✈❡③ q✉❡ ♦s ❝♦♥t❡ú❞♦s ❞❡ss❛ ❞✐s❝✐♣❧✐♥❛ s❡ ❡♥❝❛❞❡✐❛♠✱ ❡ é ♥❡❝❡ssár✐❛ ❛ ❝♦♠♣r❡❡♥sã♦ ❞❡ ✉♥s ♣❛r❛ ♦ ❛♣r❡♥❞✐③❛❞♦ ❞♦s ❛ss✉♥t♦s s❡❣✉✐♥t❡s✳
✶✻
❬✳✳✳❪ ❆♦ ❝♦♥trár✐♦ ❞♦ q✉❡ s❡ ♣❡♥s❛ ❡♠ ❣❡r❛❧✱ ♣♦❞❡✲s❡ ❛✜r♠❛r q✉❡ ♣❛rt❡ s✐❣♥✐✜❝❛t✐✈❛ ❞♦s ♣r♦❜❧❡♠❛s ❞❡ ❛♣r❡♥❞✐③❛❣❡♠ ✏❞♦ ❛t✉❛❧✑ ❡♥s✐♥♦ ❞❡ ❈á❧✲ ❝✉❧♦ ❡stá ✏❢♦r❛✑ ❞❡❧❡ ❡ é ✏❛♥t❡r✐♦r✑ ✐♥❝❧✉s✐✈❡ ❛♦ s❡✉ t❡♠♣♦ ❞❡ ❡①❡❝✉çã♦✳ ◆ã♦ s❡ tr❛t❛ ❛♣❡♥❛s ❞❛ tã♦ ♣r♦♣❛❧❛❞❛ ✏❢❛❧t❛ ❞❡ ❜❛s❡✑ ❞♦s ❡st✉❞❛♥t❡s✱ ❝♦♠♦ ❛✜r♠❛ ❛ ❣r❛♥❞❡ ♠❛✐♦r✐❛ ❞♦s ♥♦ss♦s ❝♦❧❡❣❛s ♣r♦❢❡ss♦r❡s✳ ❬✳✳✳❪ ❆ss✐♠✱ ❛♦ ✐♥✈és ❞❡ s❡ ❢❛③❡r ♠❡♥çã♦ ❛ ✉♠❛ ✏❢❛❧t❛ ❞❡ ❜❛s❡✑ ❞♦s ❡s✲ t✉❞❛♥t❡s✱ ♦ q✉❡ s❡ ♣r❡❝✐s❛ ❢❛③❡r✱ ❞❡ ❢❛t♦✱ é ❡st❛❜❡❧❡❝❡r ♦s ❝♦♥❝❡✐t♦s ❜ás✐❝♦s ❡ ♥❡❝❡ssár✐♦s ♣❛r❛ s❡ ❛♣r❡♥❞❡r ❛s ✐❞❡✐❛s ❜ás✐❝❛s ❞♦ ❈á❧❝✉❧♦✳ ❬✳✳✳❪ ✭❘❊❩❊◆❉❊✱ ✷✵✵✸✱ ♣✳ ✸✶✮
❖ q✉❡ ❡st❛♠♦s ♣r♦♣♦♥❞♦ ♥❡st❡ tr❛❜❛❧❤♦ é ❛ s✐♠♣❧❡s✱ ♣♦ré♠ ✐♠♣♦rt❛♥t❡✱ ✐♥tr♦✲ ❞✉çã♦ ❞❛s ✐❞❡✐❛s ✐♥t✉✐t✐✈❛s ❞❡ ❝á❧❝✉❧♦✱ ♦✉ s❡❥❛✱ ❞❛s ✐❞❡✐❛s ❣❡r❛❞♦r❛s ❞❡ss❡s tó♣✐❝♦s ❞❡ ❡st✉❞♦ ♥♦ ❊♥s✐♥♦ ❙✉♣❡r✐♦r✳
❖ ❡♥s✐♥♦ ❞❡ ❡❧❡♠❡♥t♦s ❞❡ ❈á❧❝✉❧♦ ❉✐❢❡r❡♥❝✐❛❧ ❡ ■♥t❡❣r❛❧ ♥♦ ❡♥s✐♥♦ ♠é❞✐♦ é ❛❧❣♦ q✉❡ ❡stá ❛♦ ❛❧❝❛♥❝❡ ❞♦s ❛❧✉♥♦s ❞❡ss❡ ♥í✈❡❧ ❞❡ ❡♥s✐♥♦✱ ❞❡s❞❡ q✉❡ ♥ã♦ s❡❥❛ ❝❤❡✐♦ ❞❡ ❢♦r♠❛❧✐s♠♦s ❝♦♠♦ ♥♦s ❝✉rs♦s s✉♣❡r✐♦r❡s✳
Pr❡♣❛r❛r ♦ ❛❧✉♥♦ ❛ ♣❛rt✐r ❞♦ ♣r✐♠❡✐r♦ ❛♥♦ ❞♦ ❡♥s✐♥♦ ♠é❞✐♦ ♣❛r❛ q✉❡ s❡ ♦❜t❡♥❤❛ ❡ss❡ ❝♦♥❤❡❝✐♠❡♥t♦ é ❞❡ s✉♠❛ ✐♠♣♦rtâ♥❝✐❛✱ ♣♦✐s ❡ss❡ ❝♦♥t❡ú❞♦ s❡ ❡♥❝♦♥tr❛ ❛❧t❛♠❡♥t❡ ❝♦♥❡①♦ ❝♦♠ ❛ ❝✐ê♥❝✐❛ ♠♦❞❡r♥❛✱ ❜❡♠ ❝♦♠♦ ❛ ❡①♣❧♦r❛çã♦ ❞❡ ❝♦♠♣❡tê♥❝✐❛ ❡ ❤❛❜✐❧✐❞❛❞❡s ♠❛t❡♠át✐❝❛s q✉❡ ♣♦ss❛♠ ❛ ✈✐r s❡r ❞❡s❡♥✈♦❧✈✐❞❛s ♣❡❧♦s ♣ró♣r✐♦s ❛❧✉♥♦s✳
❊♠ s❡✉ ❛rt✐❣♦ ❈á❧❝✉❧♦ ♥♦ s❡❣✉♥❞♦ ●r❛✉✱ ♦ ♣r♦❢❡ss♦r ❘♦❜❡rt♦ ❈♦st❛❧❧❛t ❉✉❝❧♦s ✭❉❯❈▲❖❙✱ ✶✾✾✷✮✱ ❞❡❢❡♥❞❡ ♦ ❝á❧❝✉❧♦ ♥♦ ❡♥s✐♥♦ ♠é❞✐♦✱ ❞❡s❞❡ q✉❡ s❡❥❛ ❛♣r❡s❡♥t❛❞♦ ❞❡ ♠❛♥❡✐r❛ ❝♦♥✈❡♥✐❡♥t❡✳ ❙❡❣✉♥❞♦ ♦ ❛✉t♦r✱ ♦ ❈á❧❝✉❧♦✱ ❛♦ ❝♦♥trár✐♦ ❞❡ s❡r ❞✐❢í❝✐❧✱ é ♠✉✐t♦ ❣r❛t✐✜❝❛♥t❡✱ ♣♦rq✉❡ tr❛③ ✐❞❡✐❛s ✐♥♦✈❛❞♦r❛s✱ ♣❡❧♦ ♣♦❞❡r ❡ ♣❡❧♦ ❛❧❝❛♥❝❡ ❞❡ s❡✉s ♠ét♦❞♦s✳ ❆t✉❛❧♠❡♥t❡ ❛❧❣✉♥s ❧✐✈r♦s ❞✐❞át✐❝♦s ❞❡ ❡♥s✐♥♦ ♠é❞✐♦ ❛♣r❡s❡♥t❛♠ tó♣✐❝♦s r❡❧❛t✐✈♦s ❞♦ ❈á❧❝✉❧♦ ❉✐❢❡r❡♥❝✐❛❧ ❡ ■♥t❡❣r❛❧✱ ❝♦♠♦ ❧✐♠✐t❡✱ ❞❡r✐✈❛❞❛s ❡ ✐♥t❡❣r❛✐s ✭●■❖❱❆◆◆■❀ ❇❖◆✲ ❏❖❘◆❖✱ ✷✵✵✺✮ ❡ ✭P❊❙❙❖❆❀ ■❙❍■❍❆❘❆✱ ✷✵✶✶✮✳
▼❛s✱ ✐♥❢❡❧✐③♠❡♥t❡ tr❛③❡♠ ❡st❡ ❝♦♥t❡ú❞♦ ♥♦ ✸♦ ❛♥♦✱ ♦✉ s❡❥❛✱ ♥♦ ✜♥❛❧ ❞♦ ❝✉rs♦✱ ♦♥❞❡ ♣♦✉❝♦ s❡ ♣♦❞❡ ❛♣r♦✈❡✐t❛r ❞♦ ❡st✉❞♦✳ ❊♥tr❡t❛♥t♦✱ ♥❛ ♠❛✐♦r✐❛ ❞❛s ✈❡③❡s✱ ❡st❡s t❡♠❛s ♥ã♦ sã♦ ❡♥s✐♥❛❞♦s s♦❜ ♦ ♣r❡t❡①t♦ ❞❡ s❡r❡♠ ❞✐❢í❝❡✐s ❡ ✐♠♣ró♣r✐♦s✳ ❖ ❈á❧❝✉❧♦ ♣❛ss♦✉ ❛ ❢❛③❡r ♣❛rt❡ ❞♦ ❧✐✈r♦ ❞✐❞át✐❝♦✱ ♠❛s ♥ã♦ ❞♦ ❝✉rrí❝✉❧♦ ❞❡ ❡♥s✐♥♦ ♠é❞✐♦✱ ♦ q✉❡ ♦ t♦r♥❛ ❡♥tã♦✱ ♣♦✉❝♦ ✈❛❧♦r✐③❛❞♦✱ ❣❡r❛♥❞♦ ❛ss✐♠✱ ❞❡✜❝✐ê♥❝✐❛s ♥❛ ❛♣r❡♥❞✐③❛❣❡♠ q✉❡ ❛❝❛❜❛♠ r❡✢❡t✐♥❞♦ ♥♦ ❡♥s✐♥♦ s✉♣❡r✐♦r✳
P❛r❛ P❛❧✐s ✭✶✾✾✺✮✱ ♦s ❝✉rs♦s s✉♣❡r✐♦r❡s q✉❡ ❛♣r❡s❡♥t❛♠ ❛ ❞✐s❝✐♣❧✐♥❛ ❞❡ ❈á❧❝✉❧♦ ❛♣r❡s❡♥t❛♠ í♥❞✐❝❡s ❛❜s✉r❞❛♠❡♥t❡ ❡❧❡✈❛❞♦s ❞❡ ❛❜❛♥❞♦♥♦ ❡ ✐♥s✉❝❡ss♦✳ ❊st❡s í♥❞✐❝❡s✱ ♣♦r s✐ só✱ ❥á ❛♣♦♥t❛♠ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ s❡ ❜✉s❝❛r ❛❧t❡r♥❛t✐✈❛s ❞❡ ❛çã♦ ♣❡❞❛❣ó❣✐❝❛ q✉❡✱ ❛❧✐❛❞❛s ❛s ♦✉tr❛s ♠❡❞✐❞❛s✱ ♣♦ss❛♠ ❞❛r ❝♦♥t❛ ❞❡ss❡ ♣r♦❜❧❡♠❛ q✉❡✱ ❞❡s❞❡ ♠✉✐t♦s ❛♥♦s✱ s✉❜s✐st❡ ♥❛ ✉♥✐✈❡rs✐❞❛❞❡✳
✶✼
tr❛r ♥í✈❡✐s ❞❡ ❛♣r♦✈❛çã♦ s❛t✐s❢❛tór✐♦s✱ ♣❛r❛ t❛♥t♦ ❞❡✈❡♠♦s ❢❛③❡r ✉♠❛ r❡❢♦r♠✉❧❛çã♦ ♥❛ ♠❛t❡♠át✐❝❛ ❞♦ ❡♥s✐♥♦ ♠é❞✐♦✱ ✈✐st♦ q✉❡ ♦ q✉❡ t❡♠♦s ❤♦❥❡ ♥♦s ♣❛r❡❝❡ ✐♥s✉✜❝✐❡♥t❡ ♣❛r❛ q✉❡ t❡♥❤❛♠♦s ✉♠❛ ❡❞✉❝❛çã♦ ❞❡ ❡①❝❡❧ê♥❝✐❛✳
◆❡ss❡ s❡♥t✐❞♦ ♣r♦♣♦♠♦s ❛q✉✐ q✉❡ s❡ ❞❡✐①❡ ♣❛r❛ tr❛③ ❛q✉❡❧❡s ❝♦♥t❡ú❞♦s ♣r♦✲ ❣r❛♠át✐❝♦s q✉❡ sã♦ ❜❡♠ ❡①t❡♥s♦s✱ ❡ ❢❛③❡r ❡♥tã♦ ✉♠❛ ♠✉❞❛♥ç❛ ♥♦ q✉❡ ❞✐③ r❡s♣❡✐t♦ ❛♦ ❡♥s✐♥♦ ❞❛ ♠❛t❡♠át✐❝❛ ♥♦ ❡♥s✐♥♦ ♠é❞✐♦✱ ✐♥s❡r✐♥❞♦ ❛ ♣r♦❜❧❡♠át✐❝❛ ❞♦ ❧✐♠✐t❡✱ ❞❡r✐✈❛❞❛s ❡ ✐♥t❡❣r❛❧✱ ❧♦❣✐❝❛♠❡♥t❡ q✉❡ s❡ ❞❡✈❡♠ ♠♦str❛r ❛❧❣✉♠❛s ❛♣❧✐❝❛çõ❡s✱ ♣❛r❛ q✉❡ ♦ ❛❧✉♥♦ ♣❡r❝❡❜❛ ♦ q✉ã♦ ✐♥t❡r❡ss❛♥t❡ ♣♦❞❡ s❡r s❡ ❞❡❞✐❝❛r ❛♦ ❡st✉❞♦ ❞❛ ♠❛t❡♠át✐❝❛✳
➪✈✐❧❛ ✭✶✾✾✶✮ ❞❡st❛❝❛ q✉❡ ❛ ❥✉st✐✜❝❛t✐✈❛ q✉❡ ♦s ♣r♦❣r❛♠❛s ❞❡ ♠❛t❡♠át✐❝❛ sã♦ ❡①t❡♥s♦s ❡ ♥ã♦ ❝♦♠♣♦rt❛r✐❛♠ ❛ ✐♥❝❧✉sã♦ ❞♦ ❝á❧❝✉❧♦ é ✉♠ ❡q✉í✈♦❝♦✳ ❙❡❣✉♥❞♦ ♦ ❛✉t♦r✱ ♦s ♣r♦❣r❛♠❛s ❡stã♦ ♠❛❧ ❡str✉t✉r❛❞♦s✳ P❛r❛ ♦ ❛✉t♦r✱ ♦s ♣r♦❢❡ss♦r❡s ✐♥s✐st❡♠ ❡♠ ❡①❡r❝❡r ♣r♦❣r❛♠❛s ❧♦♥❣♦s✱ ❝♦♠ ❝♦♥t❡ú❞♦s ❢r❛❣♠❡♥t❛❞♦s s❡♠ s✐❣♥✐✜❝❛❞♦s✳ ❊♠ s✉❛ ♦♣✐♥✐ã♦✱ ❛♣r♦✈❡✐t❛r ♦ t❡♠♣♦ ❝♦♠ ♦ ❡♥s✐♥♦ ❞❛s ♥♦çõ❡s ❜ás✐❝❛s ❞♦ ❈á❧❝✉❧♦ ❡ s✉❛s ❛♣❧✐❝❛çõ❡s s❡r✐❛ ♠❛✐s ♣r♦✈❡✐t♦s♦✳
❯♠ ❣r❛♥❞❡ ♣r♦❜❧❡♠❛ q✉❡ ✈❡♠♦s é q✉❡ ♣❛r❛ ♠✉✐t♦s ❛ ♠❛t❡♠át✐❝❛ é ✈✐st❛ ❝♦♠♦ ✉♠❛ ❝✐ê♥❝✐❛ ♣r♦♥t❛ ❡ ❛❝❛❜❛❞❛ ❡ ♥ã♦ ❝♦♠♦ ✉♠❛ ❢❡rr❛♠❡♥t❛ ✐♠♣♦rt❛♥t❡ ♣❛r❛ ♦ ❡♥t❡♥✲ ❞✐♠❡♥t♦ ❞❡ ✈ár✐❛s ❞✐s❝✐♣❧✐♥❛s✳ ❆❧é♠ ❞✐ss♦✱ ♣♦❞❡ tr❛③❡r ♦ ❛❧✉♥♦ ♣❛r❛ ✉♠ ✉♥✐✈❡rs♦ ❞❡ s❛t✐s❢❛çã♦ ♣❡❧♦ ❢❛t♦ ❞❡ ❡♥t❡♥❞❡r q✉❡ ❛ ♠❛t❡♠át✐❝❛ ♥ã♦ é ✉♠❛ ❞✐s❝✐♣❧✐♥❛ ✐♠♣♦ssí✈❡❧ ❞❡ s❡ ❛♣r❡♥❞❡r ❡ ❞❡ ❞✐❢í❝✐❧ ❛♣❧✐❝❛çã♦✳
❆ Pr♦♣♦st❛ ❈✉rr✐❝✉❧❛r ❞❡ ❙❛♥t❛ ❈❛t❛r✐♥❛ ❛✜r♠❛ q✉❡✿
❆ ▼❛t❡♠át✐❝❛ ❛✐♥❞❛ é ✈✐st❛ s♦♠❡♥t❡ ❝♦♠♦ ✉♠❛ ❝✐ê♥❝✐❛ ❡①❛t❛ ✲ ♣r♦♥t❛ ❡ ❛❝❛❜❛❞❛✱ ❝✉❥♦ ❡♥s✐♥♦ ❡ ❛♣r❡♥❞✐③❛❣❡♠ s❡ ❞ã♦ ♣❡❧❛ ♠❡♠♦r✐③❛çã♦ ♦✉ ♣♦r r❡♣❡t✐çã♦ ♠❡❝â♥✐❝❛ ❞❡ ❡①❡r❝í❝✐♦s ❞❡ ✜①❛çã♦✱ ♣r✐✈✐❧❡❣✐❛♥❞♦ ♦ ✉s♦ ❞❡ r❡❣r❛s ❡ ❵♠❛❝❡t❡s✬✳ ❬✳✳✳❪ ❛ ▼❛t❡♠át✐❝❛ é ❡♥t❡♥❞✐❞❛ ❛♣❡♥❛s ❝♦♠♦ ❢❡rr❛♠❡♥t❛ ♣❛r❛ ❛ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ♦✉ ❝♦♠♦ ♥❡❝❡ssár✐❛ ♣❛r❛ ❛ss❡❣✉r❛r ❛ ❝♦♥t✐♥✉✐❞❛❞❡ ❧✐♥❡❛r ❞♦ ♣r♦❝❡ss♦ ❞❡ ❡s❝♦❧❛r✐③❛çã♦✱ ♥ã♦ ❝♦♥✲ t❡♠♣❧❛♥❞♦ ❛ ♠✉❧t✐♣❧✐❝✐❞❛❞❡ ❞❡ ❢❛t♦r❡s ♥❡❝❡ssár✐♦s ❛♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ✉♠❛ ❡❢❡t✐✈❛ ❡❞✉❝❛çã♦ ▼❛t❡♠át✐❝❛ ✭❙❆◆❚❆ ❈❆❚❆❘■◆❆✱ ✶✾✾✽✱ ♣✳ ✶✵✺✮✳
➱ ❡✈✐❞❡♥t❡ q✉❡✱ ❝♦♠ ❡ss❡ ♣❡♥s❛♠❡♥t♦✱ ♦ ❡♥s✐♥♦ ❞❡ q✉❛❧q✉❡r ✉♠ ❞♦s ❡❧❡♠❡♥t♦s ❜ás✐❝♦s ❞♦ ❈á❧❝✉❧♦ s❡r✐❛ ♠✉✐t♦ t♦r♠❡♥t♦s♦ ♣❛r❛ ♦ ❛❧✉♥♦ ❞♦ ❊♥s✐♥♦ ▼é❞✐♦✳ P♦ré♠✱ ✉♠ ❡♥s✐♥♦ ❢❡✐t♦ ❞❡ ♠❛♥❡✐r❛ ❝♦♥t❡①t✉❛❧✐③❛❞❛ ❡ ✐♥t❡❣r❛❞❛ ❛ ✉♠ ❝♦♥t❡①t♦ r❡❛❧ é ✉♠❛ s❛í❞❛ ♣♦ssí✈❡❧ ♣❛r❛ ♦ ❡♥s✐♥♦ ❞❡ ❧✐♠✐t❡✱ ♣♦r ❡①❡♠♣❧♦✳
✶✽
♠❡❝❛♥✐s♠♦s ♣❛r❛ ❡❢❡t✉❛r ❝á❧❝✉❧♦s✱ ♠✉✐t❛s ✈❡③❡s ❞❡s❝♦♥❡❝t❛❞♦s ❞❡ q✉❛❧q✉❡r ♣r♦❜❧❡♠❛ ❞❡ ✉t✐❧✐❞❛❞❡ r❡❛❧✱ ♣♦❞❡rá s❡r ❛❜❛♥❞♦♥❛❞❛✳
❘❡③❡♥❞❡ ✭✷✵✵✸✱ ♣✳ ✶✸✮✱ ❞❡st❛❝❛ ❛ ❡❞✉❝❛çã♦ ❜ás✐❝❛ ❝♦♠♦ ✉♠ ❛❣❡♥t❡ ❞❡ ✐♠♣♦r✲ t❛♥t❡ ✐♥✢✉ê♥❝✐❛ ♥❛ ❞❡t❡r♠✐♥❛çã♦ ❞❡ ❞✐✜❝✉❧❞❛❞❡s ❡♠ ❈á❧❝✉❧♦ ❡ ❞❡ s❡✉ ❡♥s✐♥♦✳
❆♥t❡s ❞❡ t✉❞♦ ❝❛❜❡ ❞❡st❛❝❛r q✉❡ ❛ ♠❛✐♦r ♣❛rt❡ ❞♦ t❡rr✐tór✐♦ ❞♦ ❧✉❣❛r✲ ♠❛tr✐③ ❞❛s ❞✐✜❝✉❧❞❛❞❡s ❞❡ ❛♣r❡♥❞✐③❛❣❡♠ ❞♦ ❡♥s✐♥♦ s✉♣❡r✐♦r ❈á❧❝✉❧♦ ❡♥❝♦♥tr❛✲s❡ ♥♦ ❡♥s✐♥♦ ❜ás✐❝♦✳ ❆ ❡✈✐t❛çã♦✴❛✉sê♥❝✐❛ ❞❛s ✐❞❡✐❛s ❡ ♣r♦✲ ❜❧❡♠❛s ❝♦♥str✉t♦r❡s ❞♦ ❈á❧❝✉❧♦ ♥♦ ❡♥s✐♥♦ ❜ás✐❝♦ ❞❡ ♠❛t❡♠át✐❝❛ ❝♦♥s✲ t✐t✉✐✱ ❡❢❡t✐✈❛♠❡♥t❡✱ ♦ ♠❛✐♦r ♦❜stá❝✉❧♦ ❞❡ ♥❛t✉r❡③❛ ❡♣✐st❡♠♦❧ó❣✐❝❛ ❞♦ ❡♥s✐♥♦ ❞❡ ❈á❧❝✉❧♦✱ ❡ ♣♦rq✉❡ ♥ã♦ ❞✐③❡r ❞♦ ♣ró♣r✐♦ ❡♥s✐♥♦ ❞❡ ♠❛t❡♠á✲ t✐❝❛✳ ➱ ✐♥❝♦♠♣r❡❡♥sí✈❡❧ q✉❡ ♦ ❈á❧❝✉❧♦✱ ❝♦♥❤❡❝✐♠❡♥t♦ tã♦ ✐♠♣♦rt❛♥t❡ ♣❛r❛ ❛ ❝♦♥str✉çã♦ ❡ ❡✈♦❧✉çã♦ ❞♦ ♣ró♣r✐♦ ❝♦♥❤❡❝✐♠❡♥t♦ ♠❛t❡♠át✐❝♦✱ ♥ã♦ ♣❛rt✐❝✐♣❡ ❞♦ ❡♥s✐♥♦ ❞❡ ♠❛t❡♠át✐❝❛✳ ❖ ❝á❧❝✉❧♦ é✱ ♠❡t❛❢♦r✐❝❛♠❡♥t❡ ❢❛❧❛♥❞♦✱ ❛ ❡s♣✐♥❤❛ ❞♦rs❛❧ ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦ ♠❛t❡♠át✐❝♦ ✭❘❊❩❊◆❉❊✱ ✷✵✵✸✱ ♣✳ ✶✸✮✳
❯♠❛ ❞❛s ❝❛✉s❛s ❞❡ ♦ ❈á❧❝✉❧♦ s❡r ✈✐st♦ ❝♦♠♦ ❛❧❣♦ ❞✐❢í❝✐❧ ❡stá r❡❧❛❝✐♦♥❛❞♦ ❝♦♠ ❛ ❝♦♥str✉çã♦ ❞❛ ❛♣r❡♥❞✐③❛❣❡♠ ❞❡s❞❡ q✉❡ ❛ ❝r✐❛♥ç❛ ♠❛tr✐❝✉❧❛✲s❡ ♥❛ ❡s❝♦❧❛✱ ✉♠❛ ✈❡③ q✉❡ ♦s ♣r♦❢❡ss♦r❡s ❞♦ ❊♥s✐♥♦ ❋✉♥❞❛♠❡♥t❛❧✱ ❡♠ ❣❡r❛❧ ♥ã♦ ❞❡s❡♥✈♦❧✈❡♠ ❝♦♠ ❛s ❝r✐❛♥ç❛s ❛ ❝✉r✐♦s✐❞❛❞❡ ❡♠ s❛❜❡r ❝♦♠♦ t❡✈❡ ♦r✐❣❡♠ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ q✉❡ ❡stá s❡♥❞♦ ❡st✉❞❛❞♦✳
❙❡♥❞♦ ❛ ♠❛t❡♠át✐❝❛ ✉♠❛ ❞✐s❝✐♣❧✐♥❛ ♦♥❞❡ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ é ❛❝✉♠✉❧❛t✐✈♦ ❡ s❡✲ q✉❡♥❝✐❛❧✱ s❡r✐❛ ♥❡❝❡ssár✐♦ q✉❡ ❞❡s❞❡ ❛s sér✐❡s ✐♥✐❝✐❛✐s ❢♦ss❡ ❞❡s❡♥✈♦❧✈✐❞♦ ♦ ❣♦st♦ ❞❛s ❝r✐❛♥ç❛s ❡♠ ♣❡r❝❡❜❡r q✉❡ ❛ ♠❛t❡♠át✐❝❛ é ♠❛✐s q✉❡ ✉♠ ❛♠♦♥t♦❛❞♦ ❞❡ ♥ú♠❡r♦s ❡ r❡s♦✲ ❧✉çã♦ ❞❡ ✏❝♦♥t✐♥❤❛s✑✱ ♠❛s ♣r✐♥❝✐♣❛❧♠❡♥t❡ ✉♠❛ ❢♦r♠❛ ❞❡ r❛❝✐♦❝✐♥❛r s♦❜r❡ ❞❡t❡r♠✐♥❛❞❛s s✐t✉❛çõ❡s✳
❖ q✉❡ ❡♥t❡♥❞❡♠♦s t❡r s✐❞♦ ✉♠ ❡q✉í✈♦❝♦✱ ❡♠ t❡♠♣♦s ❛✐♥❞❛ r❡❝❡♥t❡s✱ ❞❡✈❡ s❡r r❡♣❡♥s❛❞♦✱ ♣♦✐s ❡♠ ♥♦ss❛ ✈✐sã♦✱ ❡♥q✉❛♥t♦ ♦s ❡st✉❞❛♥t❡s ♣❡♥s❛r❡♠ ♥❛ ♠❛t❡♠át✐❝❛ ❝♦♠♦ s✐♥ô♥✐♠♦ ❞❡ ❞✐✜❝✉❧❞❛❞❡ ♥ã♦ ❝♦♥s❡❣✉✐r❡♠♦s ❛✈❛♥ç❛r ♥♦ ❝♦♥❤❡❝✐♠❡♥t♦ ♠❛t❡♠át✐❝♦ ❥✉♥t♦ ❛ ❡❧❡s✳
❖ ❝♦♥❝❡✐t♦ ❞❡ ❞❡r✐✈❛❞❛ ❥á ❢❡③ ♣❛rt❡ ❞♦s ❝✉rrí❝✉❧♦s ❞❛s ❡s❝♦❧❛s s❡❝✉♥❞ár✐❛s ❤á ❛❧❣✉♠❛s ❞é❝❛❞❛s✳ ❍♦❥❡✱ ❡stá ♣r❡s❡♥t❡ ♥♦ ❝✉rrí❝✉❧♦ ❞❡ ✉♠ ♣❡q✉❡♥♦ ❣r✉♣♦ ❞❡ ❡s❝♦❧❛s ❞❡ ❊♥s✐♥♦ ▼é❞✐♦✳ ❖s ♣♦✉❝♦s ❧✐✈r♦s ❞✐❞át✐❝♦s✱ ♣♦r ❡①❡♠♣❧♦✱ ✭●✉❡❧❧✐✱ ✷✵✵✸❀ ▼❛❝❤❛❞♦✱ ❆✳❙✳ ✶✾✾✶❀ ■❡③③✐✱ ●✳✱ ▼✉r❛❦❛♠✐✱ ❈✳ ✫ ▼❛❝❤❛❞♦✱ ◆✳❏✳ ✷✵✵✷✮ q✉❡ r❡s❡r✈❛♠ ❛❧❣✉♥s ❝❛♣ít✉❧♦s ♣❛r❛ tr❛t❛r ❞♦ ❛ss✉♥t♦ ❢❛③❡♠✲♥♦ ❛tr❛✈és ❞❡ ✉♠❛ ❛❜♦r❞❛❣❡♠ tr❛❞✐❝✐♦♥❛❧ ❞♦ ❝♦♥❝❡✐t♦✱ ♦✉ s❡❥❛✱ ♣❛rt❡♠ ❞❛ ❞❡✜♥✐çã♦ ❢♦r♠❛❧ ✉s❛♥❞♦ ❛ ♥♦çã♦ ❞❡ ❧✐♠✐t❡✳
✶✾
❛♣r❡s❡♥t❛çã♦✱ ♦✉ s❡❥❛✱ ✐♥tr♦❞✉③✐r ♦ ❝♦♥❝❡✐t♦ ❞❡ ❞❡r✐✈❛❞❛ ♣❡❧❛ ❞❡✜♥✐çã♦ ❢♦r♠❛❧✱ ♣♦❞❡ s❡ t♦r♥❛r tã♦ ❞✐❢í❝✐❧ ♣❛r❛ ♦ ❡st✉❞❛♥t❡✱ q✉❡✱ ♥❛ ♠❛✐♦r✐❛ ❞❛s ✈❡③❡s✱ ❛❝❛❜❛ s❡ r❡str✐♥❣✐♥❞♦ às r❡❣r❛s ❞❡ ❞❡r✐✈❛çã♦✳
❆ss✐♠✱ ❡♥t❡♥❞❡♠♦s q✉❡ ❡stá ♠❛✐s ❞♦ q✉❡ ♥❛ ❤♦r❛ ❞❡ r❡❛❧✐③❛r♠♦s ✉♠❛ ❛✉t♦✲ ❛✈❛❧✐❛çã♦ ❞❡ ♥♦ss❛s ♣rát✐❝❛s ❞♦❝❡♥t❡s ❡ ♣r♦❝✉r❛r♠♦s ✉♠❛ ♥♦✈❛ ❛❜♦r❞❛❣❡♠ ♣❛r❛ ❛ ♠❛✲ t❡♠át✐❝❛ ♥♦ ❡♥s✐♥♦ ❢✉♥❞❛♠❡♥t❛❧ ❡ ♠é❞✐♦✱ ♦♥❞❡ ♦s ❡st✉❞❛♥t❡s ❝♦♥s✐❣❛♠ ♣❡r❝❡❜❡r ♦♥❞❡ ♣♦❞❡♠ ❛♣❧✐❝❛r ❡ q✉❛❧ ❛ ✉t✐❧✐❞❛❞❡ ❞❛ ♠❛t❡♠át✐❝❛ ♥❛ ✈✐❞❛ ❝♦t✐❞✐❛♥❛✳ ➪✈✐❧❛ ✭✶✾✾✶✱ ♣✳ ✷✮ r❡s✉♠❡ ❜❡♠ ❛ ✐♠♣♦rtâ♥❝✐❛ ❞♦ ❈á❧❝✉❧♦ ♥♦ ❊♥s✐♥♦ ♠é❞✐♦✿
❖ ❈á❧❝✉❧♦ é ♠♦❞❡r♥♦ ♣♦rq✉❡ tr❛③ ✐❞❡✐❛s ♥♦✈❛s✱ ❞✐❢❡r❡♥t❡s ❞♦ q✉❡ ♦ ❛❧✉♥♦ ❞❡ ✷◦ ❣r❛✉ ❡♥❝♦♥tr❛ ♥❛s ♦✉tr❛s ❝♦✐s❛s q✉❡ ❛♣r❡♥❞❡ ❡♠ ❆r✐t♠é✲ t✐❝❛✱ ➪❧❣❡❜r❛✱ ●❡♦♠❡tr✐❛✱ ❚r✐❣♦♥♦♠❡tr✐❛ ❡ ●❡♦♠❡tr✐❛ ❆♥❛❧ít✐❝❛✳ ◆ã♦ ❛♣❡♥❛s ♥♦✈❛s✱ ♠❛s ✐❞❡✐❛s q✉❡ tê♠ ❣r❛♥❞❡ r❡❧❡✈â♥❝✐❛ ♥✉♠❛ ✈❛r✐❡❞❛❞❡ ❞❡ ❛♣❧✐❝❛çõ❡s ❝✐❡♥tí✜❝❛s ♥♦ ♠✉♥❞♦ ♠♦❞❡r♥♦✳ ❖r❛✱ ♦ ♦❜❥❡t✐✈♦ ♣r✐♥❝✐♣❛❧ ❞♦ ❡♥s✐♥♦ ♥ã♦ é ♦✉tr♦ s❡♥ã♦ ♣r❡♣❛r❛r ♦ ❥♦✈❡♠ ♣❛r❛ s❡ ✐♥t❡❣r❛r ♠❛✐s ❛❞❡q✉❛❞❛♠❡♥t❡ à s♦❝✐❡❞❛❞❡✳ ◆ã♦ s❡ ✈✐s❛✱ ❝♦♠ ♦ ❡♥s✐♥♦ ❞❛ ▼❛t❡♠át✐❝❛ ♥♦ ✷◦ ❣r❛✉✱ ❢♦r♠❛r ❡s♣❡❝✐❛❧✐st❛s ♥♦ ❛ss✉♥t♦✳ ❊♥s✐♥❛✲s❡ ▼❛t❡♠át✐❝❛ ♣♦rq✉❡ ❡st❛ é ✉♠❛ ❞✐s❝✐♣❧✐♥❛ q✉❡ ❢❛③ ♣❛rt❡ s✐❣♥✐✜❝❛t✐✈❛ ❞❛ ❡①♣❡r✐ê♥❝✐❛ ❤✉♠❛♥❛ ❛♦ ❧♦♥❣♦ ❞♦s sé❝✉❧♦s✱ ♣♦rq✉❡ ❡❧❛ ❝♦♥t✐♥✉❛ s❡♥❞♦ ❤♦❥❡✱ ❝♦♠ ✐♥t❡♥s✐❞❛❞❡ ❛✐♥❞❛ ♠❛✐♦r ❞♦ q✉❡ ♥♦ ♣❛ss❛❞♦✱ ✉♠ ✐♥str✉♠❡♥t♦ ❡✜❝❛③ ❡ ✐♥❞✐s♣❡♥sá✈❡❧ ♣❛r❛ ♦s ♦✉tr♦s r❛♠♦s ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦✳
❉❡st❛ ❢♦r♠❛ ❛ ♠❛t❡♠át✐❝❛ ♣♦❞❡r✐❛ t♦r♥❛r✲s❡ ♠✉✐t♦ ♣r❛③❡r♦s❛ ❞❡ s❡r ❛♣r❡♥❞✐❞❛✳ ❈♦♠ ✐ss♦✱ ♣♦❞❡rí❛♠♦s ❞❛r ✐♥í❝✐♦ ❛ ✉♠ ♣r♦❝❡ss♦ ❞❡ ♠✉❞❛♥ç❛s ♥❛ ✈✐sã♦ q✉❡ ♦s ❛❧✉♥♦s tê♠ ❞❛ ♠❛t❡♠át✐❝❛✱ ❡♥t❡♥❞❡♥❞♦ ❛ ♠❡s♠❛✱ ♥ã♦ ♠❛✐s ❝♦♠♦ ❛❧❣♦ ❞✐❢í❝✐❧ ❡ ❞✐st❛♥t❡✱ ♠❛s q✉❡ ❡stá ♣r❡s❡♥t❡ ❡ é ✐♥❞✐s♣❡♥sá✈❡❧ ♥❛ ✈✐❞❛ ❝♦t✐❞✐❛♥❛ ❞❡ ❝❛❞❛ ✉♠ ❞❡ ♥ós✳
✷✵
Cap´ıtulo
2
❋❯◆➬➹❖✿ P❘➱✲❘❊◗❯■❙■❚❖
❋❯◆❉❆▼❊◆❚❆▲ P❆❘❆ ❖ ❊❙❚❯❉❖ ❉❖
❈➪▲❈❯▲❖
❬✳✳✳❪ ❆ ❣❡♥❡r❛❧✐③❛çã♦ ❞❛ ♥♦çã♦ ❞❡ ❢✉♥çã♦ s❡ ❞❡✈❡ ❛♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ ❢ís✐❝❛ ❛♣ós ●❛❧✐❧❡✉ ❡ ❉❡s❝❛rt❡s✳ ❆ ✐❞❡✐❛ ❞❡ ✉♠❛ ✈❛r✐❛çã♦ ❡♠ ❢✉♥çã♦ ❞♦ t❡♠♣♦ ✭q✉❡ ❉❡s❝❛rt❡s ❤❛✈✐❛ ❡①❝❧✉í❞♦ ❞❛ ❣❡♦♠❡tr✐❛✮ é ❢✉♥❞❛♠❡♥t❛❧ ♥♦s tr❛❜❛❧❤♦s ❞❡ ●❛❧✐❧❡✉✱ ♦♥❞❡ ❥á ❡♥❝♦♥tr❛♠♦s ✉♠❛ ❝❡rt❛ ♥♦çã♦ ❞❡ ❢✉♥çã♦✱ ♥♦ s❡♥t✐❞♦ ❞❡ ✉♠❛ ❛ss♦❝✐❛çã♦ ❡♥tr❡ ❞✉❛s ✈❛r✐❛❜✐❧✐❞❛❞❡s✱ ❞❛❞❛ ♣♦r ✉♠❛ ❧❡✐ ❞❡ ✈❛r✐❛çã♦ q✉❡ é ❡♥❝❛r❛❞❛ ❝♦♠♦ ✉♠ ♦❜❥❡t♦ ♠❛t❡♠át✐❝♦✳ ❬✳✳✳❪ ✭❘❖◗❯❊✱ ✷✵✵✻✱ ♣✳ ✷✮✳
❙❛❜❡♠♦s q✉❡ ♦ ❝♦♥❝❡✐t♦ ❞❡ ❢✉♥çã♦ é ✉♠ ❞♦s ♠❛✐s ✐♠♣♦rt❛♥t❡s ❞❛ ♠❛t❡♠át✐❝❛✳ ❙❡♥❞♦ q✉❡ ❡①✐st❡♠ ✈ár✐❛s ❛❜♦r❞❛❣❡♥s✱ ❞❡♣❡♥❞❡♥❞♦ ❞❛ ❢♦r♠❛ ❝♦♠♦ sã♦ ❡s❝♦❧❤✐❞♦s ♦s ❛①✐♦♠❛s✳ ❯♠❛ r❡❧❛çã♦ ❡♥tr❡ ❞♦✐s ❝♦♥❥✉♥t♦s✱ ♦♥❞❡ ❤á ✉♠❛ r❡❧❛çã♦ ❡♥tr❡ ❝❛❞❛ ✉♠ ❞❡ s❡✉s ❡❧❡♠❡♥t♦s✳ ❚❛♠❜é♠ ♣♦❞❡ s❡r ✉♠❛ ❧❡✐ q✉❡ ♣❛r❛ ❝❛❞❛ ✈❛❧♦r x é ❝♦rr❡s♣♦♥❞✐❞♦ ♣♦r
✉♠ ú♥✐❝♦ ❡❧❡♠❡♥t♦y✱ t❛♠❜é♠ ❞❡♥♦t❛❞♦ ♣♦r f(x)✳
❊①✐st❡♠ ✐♥ú♠❡r♦s t✐♣♦s ❞❡ ❢✉♥çõ❡s ♠❛t❡♠át✐❝❛s✱ ❡♥tr❡ ❛s ♣r✐♥❝✐♣❛✐s t❡♠♦s✿ ❢✉♥çã♦ tr✐❣♦♥♦♠étr✐❝❛✱ ❢✉♥çã♦ ❧✐♥❡❛r✱ ❢✉♥çã♦ ♠♦❞✉❧❛r✱ ❢✉♥çã♦ q✉❛❞rát✐❝❛✱ ❢✉♥çã♦ ❡①♣♦✲ ♥❡♥❝✐❛❧✱ ❢✉♥çã♦ ❧♦❣❛rít♠✐❝❛✱ ❢✉♥çã♦ ♣♦❧✐♥♦♠✐❛❧✱ ❞❡♥tr❡ ✐♥ú♠❡r❛s ♦✉tr❛s✳ ❈❛❞❛ ❢✉♥çã♦ é ❞❡✜♥✐❞❛ ♣♦r ❧❡✐s ❣❡♥❡r❛❧✐③❛❞❛s ❡ ♣r♦♣r✐❡❞❛❞❡s ❡s♣❡❝í✜❝❛s✳ P♦❞❡♥❞♦ ❛✐♥❞❛ s❡r ❝❧❛s✲ s✐✜❝❛❞❛s ❡♠✿ ❢✉♥çã♦ s♦❜r❡❥❡t♦r❛✱ ❢✉♥çã♦ ✐♥❥❡t♦r❛✱ ❢✉♥çã♦ ❜✐❥❡t♦r❛✱ ❧✐♠✐t❛❞❛✱ ✐❧✐♠✐t❛❞❛✱ ❡t❝✳
✷✶
❆ss✐♠✱ ✉♠❛ ❢✉♥çã♦ ❧✐❣❛ ✉♠ ❞♦♠í♥✐♦ ✭❝♦♥❥✉♥t♦ ❞❡ ✈❛❧♦r❡s ❞❡ ❡♥tr❛❞❛✮ ❝♦♠ ✉♠ s❡❣✉♥❞♦ ❝♦♥❥✉♥t♦✱ ♦ ❝♦♥tr❛❞♦♠í♥✐♦ ✭❝♦♥❥✉♥t♦ ❞❡ ✈❛❧♦r❡s ❞❡ s❛í❞❛✮✱ ❞❡ t❛❧ ❢♦r♠❛ q✉❡ ❛ ❝❛❞❛ ❡❧❡♠❡♥t♦ ❞♦ ❞♦♠í♥✐♦ ❡stá ❛ss♦❝✐❛❞♦ ❛ ❡①❛t❛♠❡♥t❡ ✉♠ ❡❧❡♠❡♥t♦ ❞♦ ❝♦♥tr❛❞♦♠í♥✐♦✳ ❖ ❝♦♥❥✉♥t♦ ❞♦s ❡❧❡♠❡♥t♦s ❞♦ ❝♦♥tr❛❞♦♠í♥✐♦✱ q✉❡ sã♦ r❡❧❛❝✐♦♥❛❞♦s ♣❡❧❛f ❛ ❛❧❣✉♠x❞♦
❞♦♠í♥✐♦✱ é ♦ ❝♦♥❥✉♥t♦ ✐♠❛❣❡♠ ♦✉ ❝❤❛♠❛❞♦ s✐♠♣❧❡s♠❡♥t❡ ✐♠❛❣❡♠✳
✷✳✶ ✲ ❊✈♦❧✉çã♦ ❤✐stór✐❝❛ ❞♦ ❝♦♥❝❡✐t♦ ❞❡ ❢✉♥çã♦
P❛r❛ ❖❧✐✈❡✐r❛ ✭✶✾✾✼✱ ♣✳ ✶✸ ❛♣✉❞ ❨♦✉s❝❤❦❡✈✐t❤✱ ✶✾✽✶✱ ♣✳ ✾✮ ♦ ❝♦♥❝❡✐t♦ ❞❡ ❢✉♥çã♦ ❝♦♠♣r❡❡♥❞❡ três ❢❛s❡s✿ ❛ ❆♥t✐❣✉✐❞❛❞❡✱ ♦♥❞❡ sã♦ ✈❡r✐✜❝❛❞♦s ❛❧❣✉♥s ❝❛s♦s ❞❡ ❞❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ ❞✉❛s q✉❛♥t✐❞❛❞❡s✱ ♦♥❞❡ ❛✐♥❞❛ ♥ã♦ s❡ ✐s♦❧♦✉ ❛s ♥♦çõ❡s ❞❡ q✉❛♥t✐❞❛❞❡s ✈❛r✐á✈❡✐s ❡ ❞❡ ❢✉♥çõ❡s✳ ❆ ✐❞❛❞❡ ▼é❞✐❛✱ ❛ q✉❛❧ s❡ ✈✐s✉❛❧✐③♦✉ ❛s ♥♦çõ❡s ❢✉♥❝✐♦♥❛✐s s♦❜ ❛ ❢♦r♠❛ ❣❡♦♠étr✐❝❛✱ ♦♥❞❡ ❝❛❞❛ ❝❛s♦ ❝♦♥❝r❡t♦ ❞❡ ❞❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ ❞✉❛s q✉❛♥t✐❞❛❞❡s ❡r❛♠ r❡♣r❡s❡♥t❛❞♦s ♣♦r ❣rá✜❝♦s ♦✉ ❞❡s❝r✐çã♦ ✈❡r❜❛❧✳ ❊ ♦ ♣❡rí♦❞♦ ▼♦❞❡r♥♦✱ ♥♦ q✉❛❧ ❝♦♠❡ç❛♠ ❛ ❛♣❛r❡❝❡r ❡①♣r❡ssõ❡s ❛♥❛❧ít✐❝❛s ❞❡ ❢✉♥çõ❡s✳
❆ ❛♥t✐❣✉✐❞❛❞❡ ❢♦✐ ❛ é♣♦❝❛ ❞♦ ♣r✐♠❡✐r♦ ❡stá❣✐♦ ❞❛ ❝♦♥❝❡♣çã♦ ❞❡ ❢✉♥çã♦✳ ❊♥❝♦♥✲ tr❛♠♦s ❡♥tr❡ ♦s ❜❛❜✐❧ô♥✐❝♦s ❡♠ ✷✵✵✵ ❛♥♦s ❛✳❈✳ t❛❜❡❧❛s ❞❡ s❡①❛❣és✐♠♦s ❞❡ q✉❛❞r❛❞♦s ❡ ❞❡ r❛í③❡s q✉❛❞r❛❞❛s✱ ❝✉❜♦s✱ r❛í③❡s✱ ❡♥tr❡ ♦✉tr♦s✳ ❊♥tr❡ ♦s ♣✐t❛❣ór✐❝♦s ❛♣❛r❡❝❡ ❛ ✐❞❡✐❛ ❞❡ ❢✉♥çã♦ ♥♦ ❡st✉❞♦ ❞❡ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ q✉❛♥t✐t❛t✐✈❛ ❞❡ ❞✐❢❡r❡♥t❡s q✉❛♥t✐❞❛❞❡s ❢ís✐❝❛s✱ ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ♦ ❝♦♠♣r✐♠❡♥t♦ ❡ ❛❧t✉r❛ ❞❛ ♥♦t❛ ❡♠✐t✐❞❛ ♣♦r ❝♦r❞❛s ❞❛ ♠❡s♠❛ ❡s♣é❝✐❡ ♣✐♥ç❛❞❛s ❝♦♠ t❡♥sõ❡s ✐❣✉❛✐s✳ ❉❡ ❛❝♦r❞♦ ❝♦♠ ❩✉✣ ✭✷✵✵✶✮✱ ❛ ♥♦çã♦ ❞❡ ❢✉♥çã♦ ♣❛r❛ ♦s ❣r❡❣♦s ❛♣❛r❡❝❡ ❡♠ ❡st✉❞♦s ❧✐❣❛❞♦s ❛ ❢❡♥ô♠❡♥♦s ❞❛ ♥❛t✉r❡③❛✳
▼❡s♠♦ ❝♦♠ ❡ss❛s ❡✈✐❞ê♥❝✐❛s✱ ♥ã♦ ❤á r❡❣✐str♦s ❝♦♥❝r❡t♦s ❞❡ q✉❡ ♦s ♣♦✈♦s ❛♥t✐❣♦s t❡♥❤❛♠ ❝r✐❛❞♦ ✉♠❛ ♥♦çã♦ ❞❡ ❢✉♥çã♦✳
◆❛ ■❞❛❞❡ ▼é❞✐❛✱ ❛ ♥♦çã♦ ❞❡ ❢✉♥çã♦ ❝♦♠❡ç❛ ❛ s✉r❣✐r ♥✉♠❛ ❢♦r♠❛ ♠❛✐s ❝♦♥❝r❡t❛✱ ♣♦✐s ♥❡ss❛ é♣♦❝❛ ◆✐❝♦❧❡ ❖r❡s♠❡ ✭✶✸✷✸✲✶✸✽✷✮ ❞❡s❡♥✈♦❧✈❡✉ ❛ t❡♦r✐❛ ❞❛s ❧❛t✐t✉❞❡s ❡ ❧♦♥✲ ❣✐t✉❞❡s ♣❛r❛ ❞❡s❝r❡✈❡r ❣r❛✉s ❞❡ ✐♥t❡♥s✐❞❛❞❡ ❞❛s ✈❛r✐á✈❡✐s ✈❡❧♦❝✐❞❛❞❡ ❡ t❡♠♣♦✳ ●❛❧✐❧❡✉ ●❛❧✐❧❡✐ ✭✶✺✻✹✲✶✻✹✷✮✱ ❡st✉❞❛♥❞♦ s♦❜r❡ ♠♦✈✐♠❡♥t♦ ❞❡ ❝♦r♣♦s ❡♠ q✉❡❞❛ ❧✐✈r❡✱ ❡①♣r❡ss♦✉ r❡❧❛çõ❡s ❢✉♥❝✐♦♥❛✐s ❛tr❛✈és ❞❛ r❡❧❛çã♦ ❡♥tr❡ ❝❛✉s❛s ❡ ❡❢❡✐t♦s✳ ❋r❛♥ç♦✐s ❱✐ét❡ ✭✶✺✹✵✲✶✻✵✸✮ ♣r♦♣ôs ❛ r❡♣r❡s❡♥t❛çã♦ s✐♠❜ó❧✐❝❛ ❞❡ ✉♠❛ q✉❛♥t✐❞❛❞❡ ❞❡s❝♦♥❤❡❝✐❞❛✱ ❢❛t♦ q✉❡ ♣♦ss✐❜✐❧✐✲ t♦✉ ❡①♣r✐♠✐r r❡❧❛çõ❡s ❛tr❛✈és ❞❡ ❢ór♠✉❧❛s ❛❧❣é❜r✐❝❛s✳
❉❡s❝❛rt❡s ✭✶✻✾✻✲✶✼✺✵✮✱ ❡♠ s❡✉s ❡st✉❞♦s s♦❜r❡ ❡q✉❛çõ❡s ✐♥❞❡t❡r♠✐♥❛❞❛s✱ ✐♥tr♦✲ ❞✉③✐✉ ❛ ✐❞❡✐❛ ❞❡ q✉❡ ✉♠❛ ❡q✉❛çã♦ ❡♠x ❡ y é ✉♠❛ ❢♦r♠❛ ❞❡ ❡①♣r❡ss❛r ✉♠❛ r❡❧❛çã♦ ❞❡
❞❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ q✉❛♥t✐❞❛❞❡s✳ ✭❊✈❡s✱ ✷✵✵✹✮✳
✷✷
❛ s✉❛ ❛❜s❝✐ss❛✱ ♦ q✉❡ ♥♦s ✜❝❛ ❝❧❛r♦ q✉❡ ❡❧❡ ❥á t❡♠ ❛ ✐❞❡✐❛ ❞♦ ❝♦♥❝❡✐t♦ ❞❡ ❢✉♥çã♦✳ P♦r ✈♦❧t❛ ❞❡ ✶✻✾✽✱ ❇❡r♥♦✉❧❧✐ ✭✶✻✻✼✲✶✼✹✽✮ ✉s❛ ❛ ♣❛❧❛✈r❛ ✏❢✉♥çã♦✑ ♣❛r❛ s❡ r❡❢❡r✐r ❛ q✉❛♥t✐❞❛❞❡s q✉❡ ❞❡♣❡♥❞❡♠ ❞❡ ✉♠❛ ✈❛r✐á✈❡❧ ❡ ♣r♦♣õ❡ ❛ ♣r✐♠❡✐r❛ ❞❡✜♥✐çã♦ ❞❡ ❢✉♥çã♦ ❝♦♠♦ ❡①♣r❡ssã♦ ❛♥❛❧ít✐❝❛✱ s❡♠ ❝♦♥str✉✐r ✉♠❛ ❢✉♥çã♦ ❛ ♣❛rt✐r ❞❛ ✈❛r✐á✈❡❧ ✐♥❞❡♣❡♥❞❡♥t❡✳ ❆ ❞❡✜♥✐çã♦ s❡❣✉♥❞♦ ❇❡r♥♦✉❧❧✐✿ ✏❈❤❛♠❛♠♦s ❞❡ ❢✉♥çã♦ ✉♠❛ ❣r❛♥❞❡③❛ ✈❛r✐á✈❡❧ ✉♠❛ q✉❛♥✲ t✐❞❛❞❡ ❝♦♠♣♦st❛ ❞❡ q✉❛❧q✉❡r ♠❛♥❡✐r❛ q✉❡ s❡❥❛ ❞❡st❛ ❣r❛♥❞❡③❛ ✈❛r✐á✈❡❧ ❡ ❝♦♥st❛♥t❡✳✑
❖ q✉❡ s❡ ♣♦❞❡ ♦❜s❡r✈❛r é q✉❡ ♦s ♠❛t❡♠át✐❝♦s ❞♦ sé❝✉❧♦ ❳❱■■■ ♥ã♦ s❡ ♣r❡♦✲ ❝✉♣❛✈❛♠ ❡♠ ❢♦r♠❛❧✐③❛r ♦ ❝♦♥❝❡✐t♦ ❞❡ ❢✉♥çã♦✱ t♦❞❛✈✐❛ ♦ ♠❡s♠♦ ♥ã♦ ♦❝♦rr❡ ♥♦ sé❝✉❧♦ ❳■❳✱ s❡❣✉♥❞♦ ❩✉✣ ✭✷✵✵✶✮✱ ❈❛✉❝❤② ✭✶✼✽✾✲✶✽✺✼✮ ❡st✉❞♦✉ ❡ ❛♣r♦❢✉♥❞♦✉ ❛ ❝♦♥❝❡♣çã♦ ❞❡ ❢✉♥çã♦✱ ♣♦ré♠ s✉❛ ❞❡✜♥✐çã♦ ❡r❛ ✐♠♣r❡❝✐s❛✳ ❈❛✉❝❤② ❞❡✜♥✐✉ ❢✉♥çã♦ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿
◗✉❛♥❞♦ q✉❛♥t✐❞❛❞❡s ✈❛r✐á✈❡✐s ❡stã♦ ❧✐❣❛❞❛s ❡♥tr❡ s✐✱ ❞❡ t❛❧ ♠♦❞♦ q✉❡✱ s❡♥❞♦ ❢♦r♥❡❝✐❞♦ ♦ ✈❛❧♦r ❞❡ ✉♠❛ ❞❡❧❛s✱ ♣♦❞❡✲s❡ ♦❜t❡r ♦s ✈❛❧♦r❡s ❞❡ t♦❞❛s ❛s ♦✉tr❛s✱ ❝♦♥❝❡❜❡✲s❡ ♥♦r♠❛❧♠❡♥t❡ ❡st❛s ❞✐✈❡rs❛s q✉❛♥t✐❞❛❞❡s ❡①♣r❡ss❛s ♣♦r ♠❡✐♦ ❞❡ ✉♠❛ ❞❡♥tr❡ ❡❧❛s✱ q✉❡ r❡❝❡❜❡✱ ❡♥tã♦✱ ♦ ♥♦♠❡ ❞❡ ✈❛r✐á✈❡❧ ✐♥❞❡♣❡♥❞❡♥t❡❀ ❡ ❛s ♦✉tr❛s q✉❛♥t✐❞❛❞❡s✱ ❡①♣r❡ss❛s ♣♦r ♠❡✐♦ ❞❛ ✈❛r✐á✈❡❧ ✐♥❞❡♣❡♥❞❡♥t❡✱ sã♦ ❛s q✉❡ s❡ ❝❤❛♠❛♠ ❞❡ ❢✉♥çõ❡s ❞❡st❛ ✈❛r✐á✈❡❧✳ ✭❈❆❯❈❍❨✱ ✶✽✷✶✱ ♣✳ ✸✶✮
❆ ♣❛❧❛✈r❛ ❢✉♥çã♦ ❢♦✐✱ ♣♦st❡r✐♦r♠❡♥t❡✱ ✉s❛❞❛ ♣♦r ❊✉❧❡r ✭✶✼✵✼✲✶✼✽✸✮ ❡♠ ♠❡❛❞♦s ❞♦ sé❝✉❧♦ ❳❱■■■ ♣❛r❛ ❞❡s❝r❡✈❡r ✉♠❛ ❡①♣r❡ssã♦ ❡♥✈♦❧✈❡♥❞♦ ✈ár✐♦s ❛r❣✉♠❡♥t♦s✱ ♥♦t❛✲ ✈❡❧♠❡♥t❡ ✐♥tr♦❞✉③✐✉ ♦ ❝♦♥❝❡✐t♦ ❞❡ ✉♠❛ ❢✉♥çã♦✱ ❡ ❢♦✐ ♦ ♣r✐♠❡✐r♦ ❛ ❡s❝r❡✈❡r f(x) ♣❛r❛
❞❡♥♦t❛r ❛ ❢✉♥çã♦ f ❛♣❧✐❝❛❞❛ ❛♦ ❛r❣✉♠❡♥t♦ x✳ ❊❧❡ t❛♠❜é♠ ✐♥tr♦❞✉③✐✉ ❛ ♥♦t❛çã♦ ♠♦✲
❞❡r♥❛ ♣❛r❛ ❛s ❢✉♥çõ❡s tr✐❣♦♥♦♠étr✐❝❛s✳
❯♠❛ ❢✉♥çã♦ ❞❡ q✉❛♥t✐❞❛❞❡ ✈❛r✐á✈❡❧ é ✉♠❛ ❡①♣r❡ssã♦ ❛♥❛❧ít✐❝❛ ❝♦♠✲ ♣♦st❛ ❞❡ q✉❛❧q✉❡r ♠♦❞♦ q✉❡ s❡❥❛✱ ♣♦r t❛❧ q✉❛♥t✐❞❛❞❡ ❡ ♣♦r ♥ú♠❡r♦s ♦✉ q✉❛♥t✐❞❛❞❡s ❝♦♥st❛♥t❡s✳ ❙❡rá✱ ♣♦✐s✱ ❢✉♥çã♦ ❞❡ z t♦❞❛ ❡①♣r❡ssã♦ ❛♥❛✲ ❧ít✐❝❛ q✉❡ ❛❧é♠ ❞❛ ✈❛r✐á✈❡❧z❝♦♥t✐✈❡r q✉❛♥t✐❞❛❞❡s ❝♦♥st❛♥t❡s✳ ❆ss✐♠✱ a+ 3z;az−4z2;az+√a2−z2;cz;❡t❝✳ sã♦ ❢✉♥çõ❡s ❞❡ ③ ✭❊❯▲❊❘✱ ✶✼✹✽✱ ♣✳ ✹✮✳
❈♦♠ ♦ t❡♠♣♦ ❢♦✐✲s❡ ❛♠♣❧✐❛♥❞♦ ❛ ❞❡✜♥✐çã♦ ❞❡ ❢✉♥çõ❡s✳ ❖s ♠❛t❡♠át✐❝♦s ❢♦r❛♠ ❝❛♣❛③❡s ❞❡ ❡st✉❞❛r ✏❡str❛♥❤♦s✑ ♦❜❥❡t♦s ♠❛t❡♠át✐❝♦s t❛✐s ❝♦♠♦ ❢✉♥çõ❡s q✉❡ ♥ã♦ sã♦ ❞✐❢❡r❡♥❝✐á✈❡✐s ❡♠ q✉❛❧q✉❡r ❞❡ s❡✉s ♣♦♥t♦s✳
❋♦✐ ❉✐r✐❝❤❧❡t ✭✶✽✵✺✲✶✽✺✾✮ q✉❡♠ ❝r✐♦✉ ❛ ❞❡✜♥✐çã♦ ✏❢♦r♠❛❧✑ ❞❡ ❢✉♥çã♦ ♠♦❞❡r♥❛ ♦ q✉❛❧ ♠❛✐s s❡ ❛♣r♦①✐♠❛ ❞♦ ♠♦❞❡❧♦ ❛t✉❛❧✿
