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1. [16.9] yields / = -(Ax + 6y)/(6x + 2y) = ~{2x + 3y)/(3x + y).

3. (a) y' = x/y = ±1. The origin must be excluded. See Fig. 44.

(b) >•' = 2x/3y2 = (2/3)x~]/3. The origin must be excluded. See Fig. 45.

FIGURE 45

fix) dt f'{x)J 'fix) fix) f(x) t+x 7. (a) U'xix, y) = F'{fix)+giy))f'ix), and U'v(x,y) = F'(fix)+giy))g/iy), so In [U'xix.y)/U'yix,y)] = In [fix)/g'iy)} = In fix) - ]ng'(y). Now the result follows easily, (b) Confirming [2] is routine. Then Axayb = where f (jc) = ln A + a lnx ^ g(y) _ b ln ^

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