Math 170B HW #5 Partial Solutions
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1. C = (e^(1.3))*(0.00211261)/6 = 0.00129197.


2. C = 1/400.


3. Need n >= 224.


4. f[x_0] = 1,  f[x_1] = 3,  f[x_0, x_1] = 5.


5a. Computational.

5b. By looking at the table, some of the terms become 0 and the 
    Lagrange interpolatory polynomial has degree 3 (not 5).


6.  By reordering the terms nicely, one gets the polynomial to be 
    5 - (x - 4) - 2(x - 4)(x - 3) + 3(x - 4)(x - 3)(x - 6).


7a. Plug into the formulas and simplify.

7b. Plug into the formulas and simplify.


8a. -1 + (x + 2) - 3(x + 2)(x) = -3x^2 - 5x + 1.

8b. -1 + (x + 2) - 3(x + 2)(x) + (x + 2)(x)(x + 1) = x^3 - 3x + 1. 
     (the point here is that when adding a data point, we don't have to 
      start all over in computing the polynomial - we simply just add one 
      more term)

8c. -3/8 and -9/4, respectively.


9. See the proof of Thm 3.3 on page 108.


10. MATLAB.