Question $3(20$ pts $)$

Consider the non$-$linear equation

$x^2+5=e^x.$

$(1)$ Suppose we want to solve it using Newton$-$Raphson method, initialize at $x_0=2,$ given the values returned by the next two iterations: $x_1$ and $x_2.$

$(2)$ Suppose we want to solve it using Bisection method, initialize at the interval $[0,3],$ given the intervals returned by the next two iterations.