Question

1. Interchange the order of integration and evaluate the integral S" S" Siny dy dx. 2. Use Lagrange multipliers to find the points on the curve x'y = 16 nearest the origin. 2 Eindholm of
question 2

Answer 1

Da f = x 9-16 distance of point (2,9, 2) form angin da bi ry + 2² det egenys) esity'tz we have to manimize g(2,9, 2) Og = (22, 2y, 22) of = (4283y, ach o) minima will occur at point Dg = af 22 zy- & A - Arnet x 23 an 22=0 3 (4 ochy-16=0 from 0 2 2n= sy 4 Ry 4 (let nzo) n foom - 2= 44² 1648-16=0 y = 1 & y = 1,2 = + 2 , 2=0 2-0, to most possible) if no,

So, 2 cases y (250) d = 4+1+0=5 2) (-2, 0) d = 4+1to 5 So there are 2 points nearest to от – (2,1,0) and (-2,1,0) the
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