SalasSV_11_06_ex - 680 ± CHAPTER 11 INFINITE SERIES...

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Unformatted text preview: 680 ± CHAPTER 11 INFINITE SERIES EXERCISES 11.6 Find the Taylor polynomial of the function f for the given values of a and n , and give the Lagrange form of the remainder. 1. f ( x ) = √ x ; a = 4, n = 3. 2. f ( x ) = cos x ; a = π/ 3, n = 4. 3. f ( x ) = sin x ; a = π/ 4, n = 4. 4. f ( x ) = ln x ; a = 1, n = 5. 5. f ( x ) = tan − 1 x ; a = 1, n = 3. 6. f ( x ) = cos π x ; a = 1 2 , n = 4. Expand g ( x ) as indicated and specify the values of x for which the expansion is valid. 7. g ( x ) = 3 x 3 − 2 x 2 + 4 x + 1 in powers of x − 1. 8. g ( x ) = x 4 − x 3 + x 2 − x + 1 in powers of x − 2. 9. g ( x ) = 2 x 5 + x 2 − 3 x − 5 in powers of x + 1. 10. g ( x ) = x − 1 in powers of x − 1. 11. g ( x ) = (1 + x ) − 1 in powers of x − 1. 12. g ( x ) = ( b + x ) − 1 in powers of x − a , a ±= − b . 13. g ( x ) = (1 − 2 x ) − 1 in powers of x + 2. 14. g ( x ) = e − 4 x in powers of x + 1....
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This note was uploaded on 10/12/2010 for the course MATH 12345 taught by Professor Smith during the Spring '10 term at University of Houston - Downtown.

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