Problem Statement: Find an approximate root of the function $f(x) = x^3 - 4x - 9$ using the Bisection Method. Perform two iterations, starting with the interval $[2, 3]$.

Problem Statement: Find an approximate root of $f(x) = e^x - 3x$ using the Bisection Method. Perform two iterations, starting with the interval $[0, 1]$.

Problem Statement: You are using the Bisection Method on the interval $[1, 2]$. Calculate the absolute maximum error bound after 4 complete iterations.

Problem Statement: Find an approximate root of the function $f(x) = x^2 - 2$ (which calculates $\sqrt{2}$) using the Newton-Raphson Method. Perform two iterations, starting with an initial guess $x_0 = 1.5$.

Problem Statement: Approximate the definite integral $\int_0^2 x^2 dx$ using the Trapezoidal Rule with $n = 4$ subintervals.

Problem Statement: Solve the ordinary differential equation $dy/dx = x + y$ with the initial condition $y(0) = 1$ using Euler's Method. Estimate $y(0.2)$ using a step size $h = 0.1$.

Problem Statement: Approximate the definite integral $\int_0^2 x^2 dx$ using Simpson's 1/3 Rule with $n = 4$ subintervals. Compare the result to the Trapezoidal rule approximation (2.75).

Problem Statement: Solve the following system of linear equations using Gaussian Elimination to transform the augmented matrix into upper triangular (Row Echelon) form, followed by back-substitution.

$2x + y = 5$ $4x + 3y = 11$