I have f1(x,y) = x^2 + 3y^2 - 1 = 0 and f2(x,y) = (x-2)^2 + (y-1)^2 - 4 = 0 I am suppossed to find the roots of these nonlinear equations using Multiple Newton-Rapson Method and I am supposed to guess the initial estimate of the roots by sketching the graphs. How do I guess them?
2026-03-28 13:40:16.1774705216
How to find initial estimate of roots from graphs?
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The functions $f_1$ and $f_2$ are an ellipse and a circle, respectively.
With a small amount of algebra you can determine center, radius, and major and minor axes by inspection. Then grab some graph paper and estimate where they intersect.