Apply numerical $($computational$)$ methods to solve and comprehend parameter, initial condition, and other function problems. Use Python to understand: Taylor Series:$$

$1.)$To approximate a function, use the Taylor series.

Plot both the original function and its first$-$order Taylor approximation. Modify it to include higher$-$order Taylor approximations.

$2.)$ Demonstrate that the general Taylor series expression simplifies to the Maclaurin series at a$=0.$