Section 2.6
2b. Applying Newton's method with p 0 = 1 gives p7 =
-3.548233, and with p0 =
4, p5 =
4.381113. Divide P (x) to get
The complex roots of this quadratic can be found by the
quadratic formula and are approximately
4b. The fol lowing table lists initial approximations and
roots using 
method.
Section 3.1
5a. n = 1: Use x1 = 8.3 and x2 =
8.6:
n = 2: Use x0 = 8.3, x1 = 8.6 and x2
= 8.7:
n = 3: Use x0 = 8.1, x1 = 8.3, x2
= 8.6 and x3 = 8.7:
7a. Neville's method with x = [8.3, 8.6, 8.7, 8.1] and f =
f(x) gives the following table:
9a. n = 1: We have f'(x) = ln x + 1 and f''(x) = 1/x, and
the error is bounded by
The true error is 
n = 2: We have 
and the
error is bounded by
Section 3.2
3a.
5a.
17 We have the formula
and substituting gives 
Using the formula
and substituting gives 
Further,
