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1330hw7-1

# 1330hw7-1 - x = π 4(use 8 decimal places 1 n x n x n 1 1 2...

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MAT 1330, Fall 2011 Assignment 7 Due Friday December 2nd at 3:00pm in the math department foyer. Late assignments will not be accepted; nor will unstapled assignments. Instructor (circle one): Robert Smith? Jason Levy Olga Vassilieva Catalin Rada 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. Use the Newton’s method to estimate the solution of the equation 2 cos( x ) - x = 0 . by completing the following steps: (a) Use the Intermediate Value Theorem to show that there exists a solution between 0 and π 2 : (b) Perform four iterations of the Newton’s method with the initial value

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Unformatted text preview: x = π 4 (use 8 decimal places). 1 n x n x n +1 1 2 3 Question 2. Suppose that the length of a snake at age t is given by the function L ( t ), which satisﬁes the following equation: dL dt = e-. 1 t , t ≥ . (a) Find L ( t ) if the limiting length L ∞ is given by L ∞ = lim t →∞ L ( t ) = 25 (inches) . . (b) How long was the snake at age t = 0? 2 . Question 3. Evaluate the following integrals. (a) Z x ln xdx . (b) Z dx x ln x . (c) Z e 2 x cos 3 x dx 3 . (d) Z x √ 2 x-1 dx . (e) Z 3 x 2 cos( x 3 ) dx . (f) Z te t 2 +1 dt 4 . (g) Z e cos x sin x dx . 5...
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