MATH 2321 Lecture 12: 2.3 Linear Approximation & Differentials
13 Feb 2019
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801. 2) f(0. 9, 1. 2) 2 l, (0. 9,1,2)=3-(0. 9-1)-3 (1. 2-1) 12. A thin metal disk is centered on the xy plane. At each point (x,y) on the disk, it has temperature t(x,y), given in c. 1 :120 + 12(x-3) - 8(x-1)] i sol. b) z = ((x,y) = 2 = 120+12(x-3) - 8(y-1) | Sol. c) t(2. 95,1. 1) 2 27 (2. 95,1. 1) = 120+12(2. 95-3)-8(1. 1-1)=(118. 6) Ex. f(x,y)=4+ x-x2-y3 : find the linearization of f(x,y) at (x,y)= 1, 1, find the linearization to approximate f(0. 9, 1. 2) sol. 1) lf(x,y) = f(a,b) + fyla, b)(x-2) + fy(a,b)(y-6). i f(1,1) + fx (1, 1)(x-1)+ fy (1, 1)(y-1). ##2. 3 linear approximation & differentials ## i ;) linearization of f(x) at x=a. L f(x)= f(a) = f"(a)(x-a). i 2) linear approximation of f(x) when his near a l a l in calc i/ii. 3) differential approximation i change in f = f(x)-f(a) = f"(a)(x-a). Af = f"(a) dx = f"(a)dx in calc ii.
