The requirements for each problem is listed below each problem. PLEASE LOOK AT ALL IMAGES. THANK YOU

$3\mathrm{.}6$ The infinite series

$f(n)={\displaystyle \underset{i=1}{\overset{n}{}}}\frac{1}{i^4}$

converges on a value of $f(n)=\frac{{}^4}{90}$ as $n$ approaches infinity. Write a program in single

precision to calculate $f(n)$ for $n=10,000$ by computing the sum from $i=1$ to $10,000.$ Then

repeat the calculation but in reverse order$-$that is$,$ from $i=10,000$ to $1$ using increments of $-1.$

In each case, compute the true percent relative error. Explain the results.

REQUIREMENTS FOR PROBLEM $1.$

$(1)$ Write a macro in Excel VBA in single precision to compute $f(n)$ for $n=10,000$ by computing the sum from $i=1$ to $10,000$;

$(2)$ Revise the macro in Excel VBA in single precision to compute $f(n)$ for $n=10,000$ by computing the sum from $i=10,000$ to $1$ using increments of $-1$;

$(3)$ In each case, compute the true percent relative error;

for both cases$)$

$(4)$ Explain the results.

$3\mathrm{.}7$ Evaluate $e^{-5}$ using two approaches

$e^{-x}=1-x+\frac{x^2}{2}-\frac{x^3}{3!}+....$

and

$e^{-x}=\frac{1}{e^x}=\frac{1}{1+x+\frac{x^2}{2}+\frac{x^3}{3!}+\text{c}\text{d}\text{o}\text{t}\text{s}}$

and compare with the true value of $6\mathrm{.}737947{10}^{-3}.$ Use $20$ terms to evaluate each series and compute true and approximate relative errors as terms are added.

REQUIREMENTS FOR PROBLEM #$2$

$(1)$ Write a macro in MatLab for using the first approach. Evaluate the values of the series of $e^{-x}$ up to $20$ terms;

$(2)$ Revise the macro in MatLab for using the second approach. Evaluate the values of the series of $e^{-x}$ up to $20$ terms;

$(3)$ In each case, compute the true and approximate relative error as terms are added;

$(4)$ Explain the results.