Question 2 (20 points): Consider the following nonlinear equation which describes a specific system: 2x²y+sin(x2)- xcos(y) = ey Eq. 1 a. Linearize Eq. 1 around the steady operating point of (1, 0.5) and provide a linear approximation of this non-linear system that could be used in a linear control system. b. Plot Eq. 1 together with the linearized version to identify a "reasonable" operating range where the model provides a good estimate of the actual system. might be used to predict impact of uncertainty in values of "x" and "y" used to estimate actual performance in f(x,y). c. Comment on what you might do to extend the model for wider range of application.

Fig: 1