quiz03_s107_solns

quiz03_s107_solns - Math 1B Quiz 3 Solutions Section 107...

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

View Full Document Right Arrow Icon

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

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

Unformatted text preview: Math 1B Quiz 3 Solutions Section 107 September 20, 2009 1. (4 points) For this problem, you will need the following information: Suppose | f 00 ( x ) | ≤ K for a ≤ x ≤ b . Then the error E T in the approximation from the Trapezoidal Rule is bounded by | E T | ≤ K ( b- a ) 3 12 n 2 . If we wanted to approximate R 1 6 x- 6 x +1 dx using the Trapezoidal approximation on n subintervals, how large would n have to be to make the approximation accurate to within . 0001? First we calculate f 00 ( x ). f ( x ) = ( x + 1)6- (6 x- 6) ( x + 1) 2 = 6 x + 6- 6 x + 6 ( x + 1) 2 = 12 ( x + 1) 2 f 00 ( x ) =- 12(2( x + 1)) ( x + 1) 4 =- 24 ( x + 1) 3 Now we must find the maximum of | f 00 ( x ) | for x ∈ [0 , 1]. On this interval f is increasing, so we only need to check the endpoints. (Careful; f is negative, so just taking the value at the right endpoint is not appropriate here.) Calculate f 00 (0) =- 24 and f 00 (1) =- 3, so | f 00 ( x ) | ≤ 24 on the interval. So we can choose K = 24....
View Full Document

This note was uploaded on 03/25/2011 for the course MATH 1B taught by Professor Reshetiken during the Fall '08 term at Berkeley.

Page1 / 2

quiz03_s107_solns - Math 1B Quiz 3 Solutions Section 107...

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