[obm-l] Cálculo - Análise

[Daniel Silva Braz <dsbraz@xxxxxxxxxxxx>]

Alguém pode me ajudar nessas...??

1) Recall that cos x = 1 - (1/2)x^2 + o(x^3) as x ->
0.
Use to prove that x^-2(1 - cos x) -> 1/2 as x -> 0.
In a similar way, find the limit of x^4(1 - cos2x -
2x^2) as x -> 0

2) The two equations (e^u cos v) = x and (e^u sin v) =
y define u and v as functions of x and y, say u =
U(x,y) and v = V(x,y). Find explicit formulas for
U(x,y) and V(x,y), valid for x > 0, and show that the
gradiend vector U(x,y) and V(x,y) are perpendicular at
each point (x,y)

3) Find the maximum and minimum distances from the
origin to curve 5x^2 + 6xy + 5y^2 = 8

Daniel S. Braz


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