Math 151A
HW #1, due Friday, January 12
- Reading: sections 1.1, 1.3, 1.4 and the matlab code given below (com-
pare with algorithm 2.1. from the textbook, page 47).
- Problems from section 2.1: #1 (with a hand calculator), #2(a) (with
a hand calculator), #7(ab), #12, #15 (for the longer calculations, you can
use one of the codes posted on the class webpage).
#1 Use the Bisection method to find p3for f(x) = โxโcos xon [0,1].
#2(a) Let f(x) = 3(x+ 1)(xโ
1
2)(xโ1). Use the Bisection method on
the following intervals to find p3:
(a) [โ2,1.5]
#7
(a) Sketch the graphs of y=xand y= 2 sin x.
(b) Use the Bisection method to find an approximation to within 10โ5to
the first positive value of xwith x= 2 sin x.
#12 Find an approximation to โ3 correct to within 10โ4using the Bi-
section Algorithm (hint: consider f(x) = x2
โ3).
#15 Find a bound for the number of iterations needed to achieve an
approximation with accuracy 10โ4to the solution of x3
โxโ1 = 0 lying
in the interval [1,2]. Find an approximation to the root with this degree of
accuracy.
1