Numerical Analysis, Fall 1999
Homework 1
Due September 15, 1999
Section 1.1 Computer can only be used on #16.
1a
8
9 (Show all work for finding P2 and R2)
16(Similar to 9 but use Derive (in Brown Hall or on main computer(Dos version)) or similar software.) On the b part, find the max(f4(x)) on [0,1] by solving f5(x) =0 (via software) for a root say c. Then compare f4(0) with f4(1) with f4(c). The bound for the error is max(f4(x))1^4/4!
26 First without loss of generality assume f(x1) < f(x2). Then trap
(c1f(x1)+c2f(x2))/(c1+c2) between two values and finish by invoking the intermediate value theorem.