$(5$ pts$)$ Task $8$: Suppose we use only the first $3$ terms from a Taylor series of

$f(x)=e^{x^2}$

to estimate the value of $e^4,$ where $x$ is a scalar variable. Consider the two Taylor series you obtained from Task $6$ and Task $7,$ which one presents an approximation that is closer to $e^4?$ Please justify your answer by evaluating the approximation values.