INSTRUCTOR 
Dr. Andrew Knyazev
Office: CU (Dravo) 620G. Phone: 556-8102.
Office hours: Tue 3pm - 6pm

NA I       Exam #3     (Chapter 4)         November 13, 1995
_______________________________________________________________________                      








1. Let f(x)= x+x  .Then f[0,1,2] =

[A]   0    [B]    1   [C]   2   [D]    3   [E]   None





2. Let f(x)= x   .Then f[0,1,2,3,4] =

[A]   0    [B]    1   [C]   2   [D]    3   [E]   None





3. Use interpolation points 0, 1, and 2, and function f(x)= x+x
Find the second order interpolation polynomial and
evaluate its value in x=-1. Then  p  (-1) =

[A] 3    [B]  4    [C]  5   [D]  6   [E]   None





4. Use interval [0,2] with 3 interpolation points 0, 1, and 2, 
and function f(x)= sin(x). 
Using Interpolation Errors Theorem 2 find the estimate 
of the absolute error when n=2 (second order interpolation)

[A]   0    [B]   1/4   [C]   1/6   [D]   1/12   [E]   None






5. Use interpolation points 0 and 1, and function f(x)= x 
Find the first order interpolation polynomial. Then the absolute
error of interpolation by this polynomial at the point x=-1 is

[A]   0    [B]    1   [C]   2   [D]    3   [E]   None









6. In the previous problem, the absolute error
of interpolation on interval [0,1] is

[A]   0    [B]    1   [C]   1/2   [D]    1/4   [E]   None




       
7. Use a mesh with h=1 and function f(x)= x 
Using O(h) accuracy finite difference formula for the
first derivative (first-derivative formula via
Taylor series) find its value at x=1:

[A] 3    [B] 4    [C] 5   [D] 6   [E]   None





8. In the previous problem, find the absolute error of  
approximation of the derivative at x=1:

[A] 3    [B] 4    [C] 5   [D] 6   [E]   None





9. Use a mesh with h=1 and function f(x)= x 
Using O(h ) accuracy finite difference formula for the
first derivative (first-derivative formula via
Taylor series) find its value at x=1:

[A] 0    [B] 1   [C] 2   [D]  3   [E]   None







10. Use a mesh with h=1 and function f(x)= x 
Using a finite difference formula for the
second derivative (second-derivative formula via
Taylor series) find its value at x=1:

[A]   0    [B]    1   [C]   2   [D]    3   [E]   None