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Unformatted text preview: a =9 . 8 m/s 2 . (a) Find the formula for the velocity and the position of the rock as a function of time. (b) Suppose the rock hits the ground after 3 seconds. How high is the tower? (c) Use the internet to ﬁnd the actual height of the tower of Pisa. Problem 5: [10 points] Consider the equation cos( x ) = x. (a) Show that the equation has at least one solution in the interval [0 ,π/ 2] . (b) Divide the interval in halves and decide in which half the solution lies. (c) Repeat the step in (b) twice more so that you ﬁnd an interval of length π/ 16 in which the solution lies. (d) Write down a general form of Newton’s method to ﬁnd the solution of the above equation. (e) Use the starting value x = 0 and compute x 4 by Newton’s method. (f) What goes wrong if you choose x = 3 π/ 2 as a starting value? Problem 6: [3 points] Use a Taylor polynomial of degree three to approximate the value of 8 . 1 1 / 3 . 1...
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This note was uploaded on 01/25/2011 for the course MAT 1330 taught by Professor Dumitriscu during the Spring '08 term at University of Ottawa.
 Spring '08
 DUMITRISCU
 Polynomials

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