2.2 - 1.73193 1.73242 1.73193 1.73218 1.73193 1.73206...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
SECTION 2.2 PAGE 38 1. a b 0.00000 1.00000 0.50000 1.00000 0.50000 0.75000 Estimate=(0 . 75 - 0 . 5) / 2 = 0 . 625. 3(a). a b 0.0000 1.0000 0.5000 1.0000 0.5000 0.7500 0.5000 0.6250 0.5625 0.6250 0.5625 0.5938 0.5781 0.5938 Estimate=0 . 5859. 9. The tricky part here is picking a starting value. Note that f 0 ( x ) = 2 x > 0 for x > 0, so f is increasing for x > 0. Since f (1) = - 2 < 0, f (2) = 1 > 0, the interval [1 , 2] brackets the interval. This is the calculation given below. You can do fewer iterations by taking a smaller bracketing interval. a b 1.00000 2.00000 1.50000 2.00000 1.50000 1.75000 1.62500 1.75000 1.68750 1.75000 1.71875 1.75000 1.71875 1.73438 1.72656 1.73438 1.73047 1.73438 1.73047 1.73242 1.73145 1.73242
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1.73193 1.73242 1.73193 1.73218 1.73193 1.73206 Estimate=1 . 73199. 11. The number of iterations required depends only on the starting interval, not the function. We want to find the smallest n such that b-a 2 n < 10-3 . This gives n > ln 3 × 10 3 ln 2 ’ 11 . 55, so n = 12. The iterations are: a b 1.00000 4.00000 1.00000 2.50000 Date : September 4, 2009. 1 2 SECTION 2.2 PAGE 38 1.00000 1.75000 1.37500 1.75000 1.37500 1.56250 1.37500 1.46875 1.37500 1.42188 1.37500 1.39844 1.37500 1.38672 1.37500 1.38086 1.37793 1.38086 1.37793 1.37939 and the estimate is 1 . 37866....
View Full Document

This note was uploaded on 10/10/2010 for the course MATH 01:640:111 taught by Professor Carey during the Spring '10 term at Saint Louis.

Page1 / 2

2.2 - 1.73193 1.73242 1.73193 1.73218 1.73193 1.73206...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online