Let us define xy(x² – y²) x² + y? f(x, y) = a. Verify that af _ y(xª – y4 + 4x²y?) (x² + y²)² b. Argue by symmetry that we must have af x(x4 – y4 – 4.x²y²) ду (x² + y²)² c. Now consider the function g1 :t+ fæ(0, t). Differentiate this with respect to t to find fæy(0, 0). Similarly, consider the function g2 : s+ fy(s, 0) and use it to find fyæ(0,0). d. Why do your answers to the above question not violate the Clairaut-Schwarz theorem? You may

Let us define xy(x² – y²) x² + y? f(x, y) = a. Verify that af _ y(xª – y4 + 4x²y?) (x² + y²)² b. Argue by symmetry that we must have af x(x4 – y4 – 4.x²y²) ду (x² + y²)² c. Now consider the function g1 :t+ fæ(0, t). Differentiate this with respect to t to find fæy(0, 0). Similarly, consider the function g2 : s+ fy(s, 0) and use it to find fyæ(0,0). d. Why do your answers to the above question not violate the Clairaut-Schwarz theorem? You may

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.5: Solution Of Cubic And Quartic Equations By Formulas (optional)

Problem 32E

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