(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let g(s,t) =<t*sqrt(s),s*cos(t)>

a) Find the Jacobian matrix of g(s,t).

b) Using the idea that a derivative is the best linear approximation to a function, use a linear approximation to estimate the value of g(1.02,0.01)

3. The attempt at a solution

d(x,y)/d(s,t) = [t/(2sqrt(s)) sqrt(s); cos(t) -s*sin(t)]

J_{g}(1,0) = [0 1; 1 0]

[0 1; 1 0] * [0; 1] = [1; 0]

To this I add

[0 1; 1 0] * [0.01; 0.02] = [0.02; 0.01]

I have,

[1.02; 0.01]. So I estimate g(1.02,0.01) to be around (1.02,0.01)?

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# Using Jacobians to get a Best Linear Approximation

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