[SOLVED] Math 132A Assignment 3R

Math 132A Assignment 3

1. Find the first three terms of the Taylor series for

at the point x0 = (1, −1)T . Evaluate the sum of these first three terms at p = (0.1, 0.01). What is the approximate difference of this with the true value of f(x0 +p)?

2. Find the first three terms of the Taylor series for

at the point x0 = (3, 4)T .

3. Determine whether or not the following matrices are positive definite:

(a)

(b)

(c)

4. Determine all minimizers (if any) of the following functions:

(a)

(b)

(c)

5. Let f(x) = x2 +cos(x). Starting with the interval [1, 2], use the golden section method to locate an interval of width 0.1 that contains the minimizer x*.

(You should use a calculator for the calculations but organize your work in a table please.)