Consider the following nonlinear system

x$=$ ax$3+$ bsin$($x$).$

a

Linearize about the operating point x$0.$ The parameters a$,$ b are positive unknown constants. Ignore

the higher order terms in the linearization.

b

Substitute x$0=1$ and a $=$ b $=2$ for the linearized function obtained in part a$.$ Evaluate your

linearization obtained in part a at the points x $=0\mathrm{.}1$ and x $=5.$

c

Compare the values obtained in part b to the actual values obtained from the original nonlinear

system $$x at x $=0\mathrm{.}1$ and x $=5.$ At which of these two points is the above linearization more

accurate? Explain why this is the case. Provide a plot generated in MATLAB for the nonlinear

and linearized functions in the domain $5<$ x $<5.$