2. The Fortran program below computes the Taylor series approximation for exp(x), for a given finite value of x. Program TaylorSeries 1 Compute Taylor series approximation for exp(x) real, dimension (1:10):: test_values integer ::i,j real : x, term, sum logical : : converge test_values =(/1.0,5.0,10.0,15.0,20.0,1.0,5.0,10.0,15.0,20.0 real, dimension (1:10):: test_values integer : : i,j real : : x, term, sum logical :: converge test_values =(/1.0,5.0,10.0,15.0,20.0,1.0,5.0,10.0,15.0,20.0/) do j=1,10x= test_values (j)i=1 term =1.0 sum =1.0 converge =.FALSE. do while (.not. converge) term =term(x/i) if ((sum+term) .ne. sum) then sum = sum + term i=i+1 else converge =. TRUE. end if end do print *, x,sum,exp(x),abs((sumexp(x))/exp(x)) end do pause ind Program TaylorSeries Modify the program to obtain one that computes approximations to cos(x). How do our results compare generally with the results we saw in class for the Taylor series for p(x)..

1. 2. The Fortran program below computes the Taylor series approximation for exp(x), for a given
finite value of x. Program TaylorSeries 1 Compute Taylor series approximation for exp(x) real,
dimension (1:10):: test_values integer ::i,j real : x, term, sum logical : : converge test_values
=(/1.0,5.0,10.0,15.0,20.0,1.0,5.0,10.0,15.0,20.0 real, dimension (1:10):: test_values integer : : i,j
real : : x, term, sum logical :: converge test_values
=(/1.0,5.0,10.0,15.0,20.0,1.0,5.0,10.0,15.0,20.0/) do j=1,10x= test_values (j)i=1 term =1.0 sum
=1.0 converge =.FALSE. do while (.not. converge) term =term(x/i) if ((sum+term) .ne. sum) then
sum = sum + term i=i+1 else converge =. TRUE. end if end do print *,
x,sum,exp(x),abs((sumexp(x))/exp(x)) end do pause ind Program TaylorSeries Modify the
program to obtain one that computes approximations to cos(x). How do our results compare
generally with the results we saw in class for the Taylor series for p(x).