Question

please ignore question b. I am unable to figure out the denominator at the moment.

1) + PO 43. In each part, confirm that the stated formula is the local linear approximation at (1,1,1). 4x (a) xyz + 2x + y +z (b) 2x - y - 2+2 Let f be a differentiable function of one variable, and let w = f(u), where u = x + 2y + 3z. Show that aw au du + + ax ay az

Answer 1

IS So 4(x,y,z) = f(2o, 7o; 20) + Dell Honza) For any f(%, 9,2) Linear Approximation at (x0,9, 20) (x-xo) + Of (4-9) oy (1,720) of + (2-20) 22/26,920) 1 Lineariter of f(x, y, z) = xyz+2. f (1,1,1)= 3 at (1,1,1) as at = 1 atl 1., oy KI,1,1) |(1,1,1) (1,1,1) 4(x,,) = 3 + 1. (x-1) +1.14-1) +1(2-1) - x2 = 1 - =yz I dz 2x = xt ytz xyz +2 Linear Approximation at (1,1,1) = x+y+z. w= f بیاہ 2x (2) a=x+2y+32. f(u) function of w=(x+2y+32) = 2(x+2y+32). 1 so a 2(x+2y+33). 2 2(x+2y +32) 3 how to = 12(x+2y +32) = 120 for w=uz. dw du we get both equal. Jw az - بیا =2u =) 6 dw =12u tu shown...

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