Consider the equation exy + cos(x + xy) 2 2y = 0, (x, y) =...

 

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Consider the equation e²x−y + cos(x² + xy) − 2 −2y = 0, (x, y) = R² Does the set of solutions of this equation in a neighborhood of the solution (0,0) implicitly define one of the components of the point (x, y) as a function of the other component? If so, compute the derivative of this function at the point 0. (Hint: Use the Dini's Theorem.) Consider the equation e²x−y + cos(x² + xy) − 2 −2y = 0, (x, y) = R² Does the set of solutions of this equation in a neighborhood of the solution (0,0) implicitly define one of the components of the point (x, y) as a function of the other component? If so, compute the derivative of this function at the point 0. (Hint: Use the Dini's Theorem.)

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