Calculate the random access memory $($RAM$)$ in megabytes necessary to store a multidimensional array that is $20\backslash$times $40\backslash$times $120.$ This array is double precision, and each value requires a $64-$bit word. Recall that a $6$The following infinite series can be used to approximate ex: x$2$x$3$ xn

ex $=1+$x$+2+3!+...+$n$!$

$($a$)$ Prove that this Maclaurin series expansion is a special case of the Taylor series expansion $[($Eq$.(4\mathrm{.}7)]$ with xi $=0$ and h $=$ x$.$

$($b$)$ Use the Taylor series to estimate f$($x$)=$ e$$x at xi$+1=1$ for x $=0\mathrm{.}2.$ Employ the zero$-,$ first$-,$ second$-,$ and third$-$order

i

versions and compute $\backslash$epsi t$$ for each case$4-$bit word $=8$ bytes and $1$ kilobyte $=210$ bytes. Assume that the index starts at $1.$