M4 (Functions of several variables) \text { a) Consider the function } g(x, y)=\frac{y \sin (x)}{x \sin (y)} \text {. } L. What is the domain of g? \text { II. Show that } \lim _{(x, y) \rightarrow(0,0)} g(x, y) \text { exists. } Hint: Power series! b) How can the function f(x, y)=\frac{x^{2}+y^{2}-x^{3} y^{3}}{x^{2}+y^{2}} \quad(x, y) \neq(0,0) be defined at (0,0) so that the resulting function is continuous on all of R²?c) Let f: R³1R be given by f(x)= 12 cos(x3)¹. Compute07 \frac{\partial^{3}}{\partial x_{1} \partial x_{2} \partial x_{3}} f(x) \text { and } \frac{\partial^{3}}{\partial x_{2} \partial x_{3} \partial x_{1}} f(x)

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