[Solved] MATH 151A Assignment 2

1. Given that each of the following sequences converges to p, show that it converges linearly:
   • The sequence is and the limit is p = 0;
   • The sequence is and the limit is p = 1;
2. Show that the following sequences converges to p, show that it converges quadratically.
3. (a) Use the Lagrange interpolation method to find a polynomial f such that

f(1) = 2, f(2) = 1, f(3) = 4, f(4) = 3.

(b) Use the Nevilles Method instead to find the same polynomial f. 4. Programming problem: Consider the following function f : [1,1] R

f(x) = |x|

• Plot the graph of the function f.
• Given n N{0}, define for 0 k n.

Let g_n(x) be the unique polynomial of degree n which results by interpolating the n + 1 data , i.e. ) for all 0 k n. Plot the functions f,g₂,g₃,g₄ and g₅ on the same graph.

• Plot the sequence {g_n(0.3)}_1n20.

1