(Solved): Calculate \( g(x, y) \), the second-order Taylor approximation to \( f(x, y)=5 \cos (x) \sin (y) \) ...

Calculate \( g(x, y) \), the second-order Taylor approximation to \( f(x, y)=5 \cos (x) \sin (y) \) at the point \( \left(\pi, \frac{\pi}{2}\right) \). (Use symbolic notation and fractions where needed.) \[ g(x, y)=-5+x^{2}-2 x \pi+\pi^{2}+y^{2}-\pi y+\frac{\pi^{2}}{4} \] Incorrect