### Homework assigned 10/25, due 11/1

### Section 4.1

Problems 2b, 4, 6, 10, 11

For problem #6, list the errors, rather than the roots.

Skip problem #10c.

For problem #11, also list the errors.

### Section 4.2

Problems 4, 6, 10, 11, 13

For problem #4, first find the root by stopping when f(x_n) < tol.
Then find the root by stopping when x_{n+1} - x_n < tol. Present
both roots and both errors. Take x = 1 as your first guess.

For #6, try first guesses of -1, -1/2, and 0. If the iteration converges,
say how many iterations it took. If it doesn't converge, say what
happened. If there are any B for which none of those first guesses
works, then find a first guess which does work.

For #10 and #11, find the true answer and find how close Newtons
method got to the true answer. How many iterations did it take?

### Section 4.3

Problems 6, 8

For #6, take x_0 = 1, x_1 = 2, tol = 1.e-15. Find the true answer and
find how close the secant method got to the true answer. How many
iterations did it take?

For #8c, give q_n for n=5,10,15,...40. Also give the relative
error (q_n - r^(n+1)/sqrt(5))/q_n.

### Modify the Newton code...

At the end of the diary for Wednesday morning's class, we tried to
find the zero of f(x) = x^2. The final iterate was 6.0 10^(-8) from
the real root. Figure out how to modify the code so that the final
iterate is within "tol" of the real root. Hand in your modified code
and show how it works for f(x) = x, f(x) = x^2, and f(x) = x^3.