In mathematics, functions can often be represented by infinite series. For example, the exponential function can be computed using this equation. Thus, as more terms are added in sequence, the approximation becomes a better and better estimate of the true value of ex$.$ Equation $($E$3\mathrm{.}2\mathrm{.}1)$ is called a Maclaurin series expansion. Starting with the simplest version, ex $=1,$ add terms one at a time to estimate e$0\mathrm{.}5.$ After each new term is added, compute the true and approximate percent relative errors. Note that the true value is e$0\mathrm{.}5=1\mathrm{.}648721....$ Add terms until the absolute value of the approximate error estimate $\backslash$epsi a falls below a prespecified error criterion $\backslash$epsi s conforming to three significant figures