Let F(x, y) = (f(x, y), g(x, y)) be a vector function from R2 to R2 with ? f(x, y) = 2e 6Y cos(y) ? g(x, y) = 2x2In(1+3y) Construct the linear approximation L(x, y) of F(x, y) at the point (2, 0). Use L(X, y) to approximate the F(2.01, -0.08) values. Give just the first coordinate of your approximation. So this question you must: 1. Compute the Jacobian J(x, y) of F(x, y). 2. Evaluate the Jacobian at point (2, O). 3. Construct the linear approximation L(x, y) of F(x, y) at point (2,0). 4. Calculate L(2.01, -0.08). 5. Even if the vector L(2.01, -0.08) has two components, submit only the first component below.Traduction Please see the file attached

Soit F(x, y) = (f(x, y), g(x, y)) une fonction vectorielle de R2 vers R2 avec . f ( x, y) = x2e by cos(y) . g(x, y) = 2x2In(1+3y) Construire l'approximation lineaire L(x, y) de F(x, y) au point (2, 0). Utilis approximer la valeurs F(2,01, -0,08). Donner juste la premiere coordon approximation. Donc cette question vous devez: 1. Calculer la jacobienne J(x, y) de F(x, y). 2. Evaluer la jacobienne au point (2, 0). 3. Construire l'approximation lineaire L(x, y) de F(x, y) au point (2, C 4. Calculer L(2,01, -0,08). 5. Meme si le vecteur L(2,01, -0,08) a deux composantes, soumett la premiere composante ci-bas. Donner votre reponse avec 4 decimales de precision