$(10$ points$)$ Assume you have computed hat$()=x+c_1{x}^3$ where $x1.$ Compute the relative

error in evaluating this function $($i$.$e$.,$ evaluate the impact of finite precision on the result$).$

Do not bound. Assume all of the following:

$($a$)$ error originates from representing $c_0,c_1,$ and $x.$

$($b$)$ arithmetic operations do introduce error.

$($c$)x^n$ incurs exponentiation error.

Start with

hat$({)}^{*}=(x^{*}+(c_1^{*}((x^{*}{)}^3{)}^{*}{)}^{*}{)}^{*}$