(Solved): Problem 2: Euler's Method Approximation (25 points) The problem with this approximation is that \( ...

Problem 2: Euler's Method Approximation (25 points) The problem with this approximation is that \( x=3 \) is relatively far from \( x=0 \). Over the interval \( [0,3] \), the function \( f(x) \) bends away from the linear appreximation function \( L o(x) \). Wo can get a better estimate by using a technique called Euler's Method. In this method, we will define a piecewise-linear function \[ E(x)=\left\{\begin{array}{ll} m_{0} x+b_{0} & \text { if } 0 \leq x \leq 1 \\ m_{1} x+b_{1} & \text { if } 1