CursoCalculoI Livro

Curso de Ca´ lculo de Uma Varia´ vel
˜
Terceira Edic¸ao senh x cos x dx dx

d dx d dx d dx d dx ex

− sen x

sen x

dx

dx d dx

d dx dx

dx

− cos x cosh x d dx

d dx x
1!

1
0!
dx d dx

dx

x2
2!
dx

d dx dx

1!
− 2 x dx

d dx x3
3!

d dx 0! x log x

d dx d dx dx d dx

3!
− 4 x dx

xn n! ··· dx 2! x3 dx

d dx d dx ··· dx Marco Cabral

(−1)nn! xn+1 dx

✐✐

❈✉rs♦ ❞❡ ❈á❧❝✉❧♦ ❞❡ ❯♠❛ ❱❛r✐á✈❡❧
❚❡r❝❡✐r❛ ❊❞✐çã♦
✶ ❞❡ ❆❣♦st♦ ❞❡ ✷✵✶✸

▼❛r❝♦ ❆✉ré❧✐♦ P❛❧✉♠❜♦ ❈❛❜r❛❧

P❤❉ ❡♠ ▼❛t❡♠át✐❝❛ ♣❡❧❛ ■♥❞✐❛♥❛ ❯♥✐✈❡rs✐t② ✖ ❊❯❆
Pr♦❢❡ss♦r ❞♦ ■♥st✐t✉t♦ ❞❡ ▼❛t❡♠át✐❝❛
❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❘✐♦ ❞❡ ❏❛♥❡✐r♦

❉❡♣❛rt❛♠❡♥t♦ ❞❡ ▼❛t❡♠át✐❝❛ ❆♣❧✐❝❛❞❛
■♥st✐t✉t♦ ❞❡ ▼❛t❡♠át✐❝❛
❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❘✐♦ ❞❡ ❏❛♥❡✐r♦
❘✐♦ ❞❡ ❏❛♥❡✐r♦ ✲ ❇r❛s✐❧
❈ó♣✐❛s sã♦ ❛✉t♦r✐③❛❞❛s ❡ ❜❡♠ ✈✐♥❞❛s✿ ❞✐✈✉❧❣✉❡ ♥♦ss♦ tr❛❜❛❧❤♦✦ ❈♦♥s✉❧t❡ ♦ sít✐♦

✇✇✇✳❧❛❜♠❛✳✉❢r❥✳❜r✴⑦♠❝❛❜r❛❧✴❧✐✈r♦s ♦✉ ❡♥tr❡ ❡♠ ❝♦♥t❛t♦
♠❛♣❝❛❜r❛❧✭❛t✮✉❢r❥✭❞♦t✮❜r✳

❝♦♠ ♦ ❛✉t♦r ❡♠

✐✐

❊st❡ tr❛❜❛❧❤♦ ❡stá ❧✐❝❡♥❝✐❛❞♦ s♦❜ ✉♠❛ ▲✐❝❡♥ç❛

❈r❡❛t✐✈❡ ❈♦♠♠♦♥s ❆tr✐❜✉✐✲

çã♦ ✭❇❨✮ ✖ ❯s♦ ◆ã♦✲❈♦♠❡r❝✐❛❧ ✭◆❈✮ ✖ ❈♦♠♣❛rt✐❧❤❛♠❡♥t♦ ♣❡❧❛ ♠❡s♠❛ ▲✐❝❡♥ç❛ ✭❙❆✮ ✸✳✵
❯♥♣♦rt❡❞✳ P❛r❛ ✈❡r ✉♠❛ ❝ó♣✐❛ ❞❡st❛ ❧✐❝❡♥ç❛✱ ✈✐s✐t❡

❝r❡❛t✐✈❡❝♦♠♠♦♥s✳♦r❣✴❧✐❝❡♥s❡s✴❜②✲♥❝✲s❛✴✸✳✵✴❜r✴
♦✉ ❡♥✈✐❡ ✉♠❛ ❝❛rt❛ ♣❛r❛ ❈r❡❛t✐✈❡ ❈♦♠♠♦♥s✱ ✶✼✶ ❙❡❝♦♥❞ ❙tr❡❡t✱ ❙✉✐t❡ ✸✵✵✱ ❙❛♥ ❋r❛♥❝✐s❝♦✱
❈❛❧✐❢♦r♥✐❛ ✾✹✶✵✺✱ ❯❙❆✳
❊st❛ ❧✐❝❡♥ç❛ ♣❡r♠✐t❡ q✉❡ ♦✉tr♦s ♣♦ss❛♠ ❝♦♣✐❛r ♦✉ r❡❞✐str✐❜✉✐r ❡st❛ ♦❜r❛ s❡♠ ✜♥s ❝♦♠❡r❝✐❛✐s✱
❛❞❛♣t❛r ❡ ❝r✐❛r ♦❜r❛s ❞❡r✐✈❛❞❛s s♦❜r❡ ❡st❛ ♦❜r❛ s❡♠ ✜♥s ❝♦♠❡r❝✐❛✐s✱ ❝♦♥t❛♥t♦ q✉❡ ❛tr✐❜✉❛♠
❝ré❞✐t♦ ❛♦ ❛✉t♦r ❡ ❞✐str✐❜✉❛♠ ❛ ♦❜r❛ r❡s✉❧t❛♥t❡ s♦❜ ❛ ♠❡s♠❛ ❧✐❝❡♥ç❛✱ ♦✉ s♦❜ ✉♠❛ ❧✐❝❡♥ç❛ s✐♠✐❧❛r à ♣r❡s❡♥t❡✳

❋✐❝❤❛ ❈❛t❛❧♦❣rá✜❝❛
❈❛❜r❛❧✱ ▼❛r❝♦ ❆✳ P✳
❈✉rs♦ ❞❡ ❈á❧❝✉❧♦ ❞❡ ❯♠❛ ❱❛r✐á✈❡❧ ✴ ▼❛r❝♦ ❈❛❜r❛❧ ✲ ❘✐♦ ❞❡ ❏❛♥❡✐r♦✿ ■♥st✐t✉t♦ ❞❡
▼❛t❡♠át✐❝❛✱ ✷✵✶✵✳
✶✳ ❈á❧❝✉❧♦

■✳ ❚ít✉❧♦
❈❉❉✿ ✺✶✷✳✺
✺✶✻✳✸

■❙❇◆ ❳❳✲❳❳❳❳✲❳❳❳✲❳

Sobre o Autor
▼❛r❝♦ ❆✉ré❧✐♦ P❛❧✉♠❜♦ ❈❛❜r❛❧ é ❝❛r✐♦❝❛ ✭♥❛t✉r❛❧ ❞♦ ❘✐♦ ❞❡ ❏❛♥❡✐r♦✮ ❡ tr✐❝♦❧♦r ✭t♦r❝❡❞♦r ❞♦
✢✉♠✐♥❡♥s❡✮✳
❋❡③ ♦ ❇❛❝❤❛r❡❧❛❞♦ ❡♠ ■♥❢♦r♠át✐❝❛ ♥❛ ❯❋❘❏✱ ♦ ▼❡str❛❞♦ ❡♠ ▼❛t❡♠át✐❝❛ ❆♣❧✐❝❛❞❛ ♥❛
❯❋❘❏ ❡ ♦ ❉♦✉t♦r❛❞♦ ❡♠ ▼❛t❡♠át✐❝❛ ♥❛ ■♥❞✐❛♥❛