EMCH $201-001-$HW # $2-$ Name:

Due: Monday$-$September $9,2024$

$(20)-$Determine the real root of $f(x)=4x^3-6x^2+7x-2\mathrm{.}3$

Using Bisection Method to locate the root. Employ initial guesses of $x_l=0$ and $x_u=1$ and iterate until the estimated error $lo{n}_a$ falls below a level of $lo{n}_a=14\%.(4$ iterations$).$ Show details of your calculations neatly for full credit.

Summary Table

$\backslash$table$[[$Iteration$,$x$\_($lower $),$x$\_($upper $),$x$\_($r$)($keep $4$ decimals$),$f$($x$\_($lower $)),$f$($x$\_($upper $)),$f$($x$\_($r$)),\backslash$epsi lon$\_($a$)(\%)],[1,,,,,,,$N$/$A$],[2,,,,,,,],[3,,,,,,,],[4,,,,,,,]]$

Note: Show the full details on a separate sheet. No credit simply for filling the tables.

$2.(20)-$Determine the real roots of $f(x)=x^3-20$ by using four iterations of Bisection Method to determine the highest root. Employ initial guesses of $x_1=1$ and $x_u=4.$ Compute the estimated error $\%lo{n}_a$ falls below a level of $lo{n}_a=7\mathrm{.}0\%.($four iterations$).$ Show details of your calculations neatly for full credit.

$\backslash$table$[[$Summary$,],[$Iteration$,$x$\_($lower $),$x$\_($upper $),$x$\_($r$)($ keep $4$ decimals $),$f$($x$\_($lower $)),$f$($x$\_($upper $)),$f$($x$\_($r$)),\backslash$epsi lon$\_($a$)(\%)],[1,,,,,,,$N$/$A$],[2,,,,,,,],[3,,,,,,,],[4,,,,,,,]]$

Note: Show the full details on a separate sheet. No credit simply for filling the tables.