Gabarito lista de calculo ii - lista 6

LISTA 06 – GABARITO

1. Encontrar [pic]' por derivação implícita:

(a) [pic] [pic]'[pic][pic]'[pic]'[pic]

(b) [pic] [pic] [pic]'[pic]' [pic][pic] e [pic]

[pic]'[pic]'[pic]'[pic]'[pic]'[pic] [pic]'[pic]

(c) [pic] [pic]'[pic]'[pic]'[pic]'[pic]

(d) [pic] [pic]'[pic]'[pic]'[pic]
[pic]'[pic]

(e) [pic] [pic]'[pic]' [pic]

[pic]'[pic]'[pic]'[pic]'[pic] [pic]'[pic]'[pic]'[pic]'[pic]

(f)[pic]'[pic]'[pic]'/[pic]

[pic]'[pic]'
[pic]'[pic]

[pic] [pic]'[pic]'
[pic]'[pic]

(g) [pic] [pic]'[pic] [pic]'[pic]'[pic]'[pic]'[pic]
[pic]'[pic]'[pic]

(h) [pic] [pic] [pic]

[pic]'[pic]' [pic]

[pic]'[pic] e [pic]'[pic]'[pic]
[pic]'[pic]' e [pic]'[pic]

[pic]'[pic]'[pic]
[pic]'[pic]'[pic]'[pic]'[pic]
[pic]'[pic]'[pic]

2. Encontre a equação da reta tangente à curva [pic] no ponto (1;2)

[pic]
[pic]'[pic]'[pic]'[pic] [pic] e [pic]
[pic]'[pic]

[pic]

3. Usando diferencial, calcule aproximadamente o valor de:

(a) [pic]

Se
[pic]

[pic]
[pic]'[pic]
[pic]
[pic]

[pic]

(b) [pic]
Se
[pic]

[pic]
[pic]'[pic]
[pic]
[pic]

[pic]

(c) cos 63º[pic]
Se, [pic]º →[pic]º[pic]
[pic]º[pic] [pic]º-------- [pic] 3º-------- ?
[pic] [pic]
[pic]'[pic]
[pic]
[pic]º[pic]

(d) [pic]
Se [pic]
[pic][pic] [pic]-------- [pic] 2 -------- ?
[pic]
[pic]'[pic]
[pic]
[pic][pic]

4. Um fabricante deseja fazer caixas abertas utilizando pedaços retangulares de papelão de 15 por 8 cm. Para tanto