Question $2(20$ points$)$: Consider the following nonlinear equation which describes a

specific system:

$2x^{2}y+sin(x^{-2})-xcos(y)=e^{-\frac{x}{y}},Eq.1$

a$.$ Linearize Eq$.1$ around the steady operating point of $(1,0\mathrm{.}5)$ 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.