$[1/4$ Points$]$

SCALCET$82\mathrm{.}4\mathrm{.}035.$

$($a$)$ For the limit $\underset{x1}{lim}(x^3+x+2)=4,$ use a graph to find the largest possible value of $$ that corresponds to $=0\mathrm{.}5.($Round your answer down to three decimal places.$)$

$($b$)$ By using a computer algebra system to solve the cubic equation $x^3+x+2=4+,$ find the largest possible value of $$ that works for any given $>0.$

$()=$

$($c$)$ Put $=0\mathrm{.}5$ in your answer to part $($b$).($Round your answer down to three decimal places.$)$

$(0\mathrm{.}5)=$

How does $(0\mathrm{.}5)$ compare with your answer to part $($a$)?$

$(0\mathrm{.}5)$ is smaller than the $$ from part $($a$).$

$(0\mathrm{.}5)$ is the same as the $$ from part $($a$).$

$(0\mathrm{.}5)$ is larger than the $$ from part $($a$).$