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Assignment 6

# Assignment 6 - MAT 1330 Fall 2010 Assignment 6 Due...

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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 defined for all x in R . Show that the equation f ( x ) = 0 has three distinct solutions. Answer: . Question 2. Use Newton’s method to approximate a solution of the equation 2 cos( x ) x = 0 . To that end, follow the steps outlined below: a) Use the intermediate value theorem in order to show that there is a solution between 0 and π 2 . . 1

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b) Perform four iterations of Newton’s method with initial value x 0 = π 4 . (Use 8 decimal places). n x n x n +1 0 1 2 3 Question 3. Follow the steps below to graph the function f ( x ) = e x 2 - 2 x +1 2 . a) Find the domain of
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