$($a$)$ the bisection method

$($b$)$ Ridders' method

$($c$)$ Steffensen's method

$($d$)$ the Newton$-$Raphson method

The events:

$($a$)$ Find $x$ that satisfies $f(x)=tanh(x-3)-0\mathrm{.}3+\frac{x}{2}=0$

$($b$)$ Find $x$ that satisfies $f(x)=0\mathrm{.}7sin(3x)+x-2=0$

$($c$)$ Find $x$ that satisfies $f(x)=(1+$erfx$)(1+x^2)-50=0$

For each equation, I guarantee that there is only one root in the interval $0x10.$ For bisection

and Ridders, you should start the bracketing at $x=0$ and $x=10.$ For Steffensen and Newton$-$

Raphson, you should start with a first guess at the midpoint $x=5.$

In each event, each contestant's score is the number of function evaluations $($of either $f$ or $f^{\text{'}})$ that

it takes before reaching the root with an absolute tolerance

Your mission: code up the methods yourselves $($i$.$e$.,$ don't use canned root$-$finding routines$),$

determine all $12$ scores, and crown the

evaluations $=0$

x $=$ x$\_$start

while True:

f$\_$x $=$ f$($x$)$

evaluations $+=1$

if abs$($f$\_$x$)$ tol:

break

x$\_$next $=$ x $-($f$\_$x$**2)/($f$($x$+$f$\_$x$)-$ f$\_$x$)$

evaluations $+=1$

if abs$($x$\_$next $-$ x$)$ tol:

break

x $=$ x$\_$next

return x$,$ evaluations

def newton$\_$raphson$\_$method$($f$,$ df$,$ x$\_$start, tol$=1$e$-$

:

evaluations $=0$

x $=$ x$\_$start

while True:

f$\_$x $=$ f$($x$)$

df$\_$x $=$ df$($x$)$

evaluations $+=2$

if abs$($f$\_$x$)$ tol:

break

x$\_$next $=$ x $-$ f$\_$x $/$ df$\_$x

if abs$($x$\_$next $-$ x$)$ tol:

break

x $=$ x$\_$next

return evaluations

#function definitions

def func$1($x$)$:

return math.tanh$($x $-3)-0\mathrm{.}3+$ x $/2$

def func$2($x$)$:

return $0\mathrm{.}7*$ math.sin$(3*$x$)+$ x $-2$

def func$3($x$)$:

return $(1+$ erf$($x$))*(1+$x$**2)-50$winner $($with the lowest total score$).$

ERROR

TypeError

Traceback $($most recent call last$)$

Cell In$[152],$ line $102$

$100$ for i$,f$ in enumerate$($function

s$)$:

$101$ if method$\_$name $==$ "Newton$-$

Raphson":

$-->102$ root, evals $=$ method$($

f$[0],$ f$[1],$ start$[0])$

$103$ else:

$104$ root, evals $=$ method$($

f$,$ start$[0],$ start$[1]$ if len$($start$)>1$

else start$[0])$

TypeError: cannot unpack non$-$iterable i

nt object

TypeError

Traceback $($most recent call last$)$

Cell In$[154],$ line $102$

$100$ for i$,$ f in enumerate$($function

s$)$:

$101$ if method$\_$name $==$ "Steffe

nsen$"$:

$-->102$ root, evals $=$ method$($

f$[0],$ f$[1],$ start$[0])$

$103$ else:

$104$ root, evals $=$ method$($

f$,$ start$[0],$ start$[1]$ if len$($start$)>$

$1$ else start$[0])$

TypeError: 'function' object is not su

bscriptable WHY AM I GETTING THESE ERRORS DEBUG