Exercicios resolvidos James Stewart vol. 2 7ª ed - ingles

186 0 CHAPTER 14 PARTIAL DERIVATIVES
35. The point (160, 10), corresponding to day 160 and a depth of 10m, lies between the isotherrnals with temperature values
of8 and 12°C. Since the point appears to be located about three-fourths the distance from the 8°C isothermal to the l2°C
isothermal, we estimate the temperature at. that p~int to be approximately 11° C. The point ( 180, 5) lies betwe~n the 16 and
20°C isothermals, very close to the 20°C level curve, so we estimate the temperature there to be about 19.5°C.
37. Near A, the level curves are very close together, indicating that the terrain is quite steep. At B, the level curves are much
farther apart, so we would expect the terrain to be much tess steep than near A, perhaps almost flat.
39.
41.
5
X
y
X
43. The level curves ~re (y - 2x) 2 = k or y = 2x ± ..Jk,
k ~ 0, a fami ly of pairs of parallel lines.
45. The level curves are vfx + y = k or y = -vlx + k, a'
family of vertical translations of the graph of the root
function y = -vx.
y
2
0
4321 0 1234
-1
-2
47. The level curves are ye~ = k or y = ke-x, a family of
exponential curves.
49. The level curves are J y 2 - x 2 = k or y 2 - x 2 = k 2 ,
k ~ 0. When k = 0 the level curve is the pair of lines
y = ±x. Fork > 0, the level curves are hyperbolas
with axis the y-axis.
0
X
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