高等数学，11题的第(2)(3)怎么做，需要过程，急，求高手
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11（2） z = √(x^2+y^2), dz = ( xdx+ydy)/ √(x^2+y^2)
⊿z = ( x0⊿x+y0⊿y)/ √(x0^2+y0^2)
= [4*0.05+3(-0.07)]/√(4^2+3^2) = -0.01/5 = -0.002
z = z0+⊿z = 5 - 0.002 = 4.998
(3) z = y^x, lnz = xlny,
z'<x>/z = lny, z'<x> = zlny = y^x lny
z'<y>/z =x/y, z'<y> = zx/y = y^x(x/y)
dz = y^x lny dx + y^x(x/y) dy
= 2ln2*0.05 + 2(1/2)(-0.03) = 0.1ln2 - 0.03 = 0.04
z = z0+dz = 2+ 0.04 = 2.04.
⊿z = ( x0⊿x+y0⊿y)/ √(x0^2+y0^2)
= [4*0.05+3(-0.07)]/√(4^2+3^2) = -0.01/5 = -0.002
z = z0+⊿z = 5 - 0.002 = 4.998
(3) z = y^x, lnz = xlny,
z'<x>/z = lny, z'<x> = zlny = y^x lny
z'<y>/z =x/y, z'<y> = zx/y = y^x(x/y)
dz = y^x lny dx + y^x(x/y) dy
= 2ln2*0.05 + 2(1/2)(-0.03) = 0.1ln2 - 0.03 = 0.04
z = z0+dz = 2+ 0.04 = 2.04.
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