$1)$ Write a program that repeatedly evaluates a n$-$th order polynomial p$($x$)=$ a$0+$ a$1*$x $+$ a$2*$x$^2+...+$ an$*$x$^$n where n $<=10$ The program inputs n$,$ ai$,$ and x from the keyboard and then prints out the corresponding value of p to the screen. The program continues to input new values of n$,$ ai$,$ x and evaluates p until a negative value for n is input, at which point the program stops.

$2)$Write a program that calculates exp$($x$)$ using the Taylor series approximation exp$\_$approx $=1+$ x $+$ x$^2/2!+$ x$^3/3!+...$ where x and error are input from the keyboard and a sufficient number of series terms are used such that abs$($ exp$\_$approx $-$ exp$($x$))<$ error. Hint: Use $*=$ in a loop to calculate x$^$i and i$!$ and print them out to the screen to verify that your loop is correct before calculating the series approximation.