homework3sol - Math 4650 Homework #3 Solutions 1.3 #7. Find...

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Unformatted text preview: Math 4650 Homework #3 Solutions 1.3 #7. Find the rates of convergence of the following functions as h 0. 1. lim h sin h h = 1. Use sin h = h- h 3 6 + , and we get sin h h- 1 = sin h- h h =- h 3 6 h + =- h 2 6 + . So its O ( h 2 ). 2. lim h 1- cos h h = 0. Use cos h = 1- h 2 2 + to get 1- cos h h = 1- 1- h 2 2 + h = h 2 + . So the order is O ( h ). 3. lim h sin h- h cos h h = 0. Use sin h = h- h 3 6 + and cos h = 1- h 2 2 + , and we find sin h- h cos h = h- h 3 6- h + h 3 2 + = h 3 3 + . Therefore sin h- h cos h h = h 2 3 + , and the order is O ( h 2 ). 4. lim h 1- e h h =- 1. Use e h = 1 + h + h 2 2 + , and get 1- e h h + 1 = 1 + h- e h h = 1 + h- 1- h- h 2 2- h =- h 2 + so that the order is O ( h ). 1.3, #8. 1. How many multiplications and additions are required to determine a sum of the form n X i =1 i X j =1 a i b j ?...
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This note was uploaded on 01/04/2011 for the course MATH 4650 taught by Professor To during the Spring '10 term at SUNY Geneseo.

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homework3sol - Math 4650 Homework #3 Solutions 1.3 #7. Find...

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