Assignment 6 Solutions

# Assignment 6 Solutions - MAT 1330, Fall 2010 Assignment 6...

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MAT 1330, Fall 2010 Assignment 6 Due Wednesday November 24, at the beginning of class. Late assignments will not be accepted; nor will unstapled assignments. Instructor (circle one): Frithjof Lutscher Angelika Welte Aziz Khanchi Robert Smith? DGD (circle one): 1 2 3 4 Student Name Student Number By signing below, you declare that this work was your own and that you have not copied from any other individual or other source. Signature Question 1. Consider the function f ( x )= x ( x + 1)( x + 2)( x + 3) which is de±ned for all x in R . Show that the equation f ! ( x ) = 0 has three distinct solutions. Answer: The function f ( x ) is continuous and di²erentiable on R . Furthermore, f (0) = f ( 1) = f ( 2) = f ( 3) = 0 . Therefore, according to Rolle’s theorem: There is some α ( 3; 2) such that f ! ( α )=0. There is some β ( 2; 1) such that f ! ( β There is some γ ( 1; 0) such that f ! ( γ . Question 2. Use Newton’s method to approximate a solution of the equation 2 cos( x ) x =0 .

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## This note was uploaded on 09/17/2011 for the course MAT 1330 taught by Professor Dumitriscu during the Fall '08 term at University of Ottawa.

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Assignment 6 Solutions - MAT 1330, Fall 2010 Assignment 6...

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