a$.$ Using the Intermediate value theorem, find at least one root for $x^3-e^x=0$ in the interval $[1,2].$

b$.$ By using the bisection method, find an approximation to a root for the given equation.$($For $4$

Consider the function $f(x)=5x^3+x^2-8.$ For initial value $p_0=1\mathrm{.}5,$ approximate a root by using Newton's Method. $($For $4$ iterations$)$

a$.$ Define the Lagrange interpolation polynomial.

b$.$

$\backslash$table$[[x_0,x_1,x_2$