Problem $1$

Create an Octave script file, hw$2$a$.$m$,$ to do the following:

A geometric series is defined as the sequence $1,$ x$,$ x $2$

$,$ x $3$

$,$ x $4$

$,....$in which the powers of x range over the

integers from $0$ to $\backslash$infty $.$ The sum of the terms in a geometric series converges to the limiting value $1/(1-$x$)$

if $||<1$; otherwise the terms diverge.

a$.$ For x$=0\mathrm{.}51,$ compute the sum of the first eleven terms in the series, and compare the

result with the limiting value. Repeat for $51$ and $101$ terms. Do this by generating a

vector of integers to use as the exponent of x; then use the sum function.

b$.$ Create a vector with $3$ elements that are the difference between limiting value and the

sum of the sequences for $11,51$ and $101$ terms.

Problem $2$:

Create an Octave script file, hw$2$b$.$m$,$ that allows the user to input the coefficients and constants of a

system of $3$ linear equations. Determine if there is a unique solution and output that solution. Your

program should also check if the answer is correct and print out a message stating it is correct.

It is up to you to decide how to input the data. To test your program, the system of equations below has

a solution x$=-1,$ y$=2$ and z$=3$

$4$x$-2$y$+3$z$=1$

x$+3$y$-4$z$=-7$

$3$x$+$y$+2$z$=5$

Problem $3$:

Create an Octave script file, hw$2$c$.$m that does the following:

When an object is falling because of gravity, the following formula can be used to determine

the distance the object falls in a specific time period.

$=122$

The variables in the formula are as follows:

d$=$ distance in meters

g$=9\mathrm{.}8$

t $=$ time in seconds

a$)$ Prompt the user for the time in seconds.

b$)$ Calculates the distance in meters it will fall at $20$ time steps from $0$ to the user$$s input time

value. Output the distances.

Converts the distances calculated in b to feet. Output the distances in feet.