Assign.#3

Assign.#3 - a =-9 . 8 m/s 2 . (a) Find the formula for the...

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Prof. SAMINA BASHIR, University of Ottawa, MAT 1330, Fall 2008 Assignment 3, due November 26, 8:30am in class Student Name Student Number DGD 1 (Monday) DGD 2 (Tuesday) DGD 3 (Wednesday) Problem 1: [2 points] Find the Taylor polynomials of degree 3 and 5 of the function f ( x ) = sin( x ) around x 0 = 0 . Problem 2: [6 points] A cow grows from 10kg to 150kg in weight in 7 years. Suppose that the weight is a diﬀerentiable function of time. (a) Why must the weight have been exactly 20kg at some time? (b) Why must the weight gain been exactly 20kg/year at some time? (c) Draw a graph of the weight versus time where the weight of 20kg occurs at 1 year and the rate of 20kg/year occurs at 5 years. (Note that the solution to part (c) is not unique.) Problem 3: [4 points] Find the indeﬁnite integral F of the function f ( t ) = 4 t 3 +2 t - 7 /t 2 . Find the antiderivative of f ( t ) that satisﬁes f (1) = 1 . Problem 4: [5 points] A rock falls from the tower of Pisa with initial velocity zero and a constant downward acceleration due to gravity of
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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.

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