Q$2)$ Write a MATLAB script to determine the positive real root of $ln(x^2)=0\mathrm{.}7$ using the Bisection

method $($Hint: plot to determine the initial values of $x_l$ and $x_u),$ iterate until Use a

table to display the results.$)$

Q$3)$ Write a MATLAB script to use the Newton$-$Raphson method to determine the root of $f(x)=$

$-0\mathrm{.}9x^2+1\mathrm{.}7x+2\mathrm{.}5$ using $x_0=5.$ Perform the computation until $|{}_a|$ is less than ${}_s=0\mathrm{.}01\%.$

Also, check your final answer by substituting the value of the estimated root in the function $f(x).$

$($Use a table to display the results.$)$

LAB Assignmentt

Q$4)$ Our goal is to fit the data shown in Table $1$ with a linear model using the built$-$in commands in

MATLAB. To do so$,$ use the polyfit command to find the coefficients $a_0$ and $a_1$ and use the polyval

command to evaluate tilde$(y)=a_0+a_{1}x.$ Display the result graphically

Table $1$: Data $1$

Q$5)$ Write a MATLAB script to implement the composite trapezoidal rule. Use the scrip to evaluate the

following integral $($with $n=100)$:

${\displaystyle \underset{0}{\overset{4}{}}}(1-e^{-x})dx$

Q$6)$ A function $f(x)$ is used to generate the following table of unequally spaced data:

Write a MATLAB script to implement the composite trapezoidal rule. Use the script to evaluate the

integral from $a=0$ to $b=1\mathrm{.}2.$