SalasSV_11_06_ex

# SalasSV_11_06_ex - 680 CHAPTER 11 INFINITE SERIES EXERCISES...

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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. 15. g ( x ) = sin x in powers of x π . 16. g ( x ) = sin x in powers of x 1 2 π . 17. g ( x ) = cos x in powers of x π . 18. g ( x ) = cos x in powers of x 1 2 π . 19. g ( x ) = sin 1 2 π x in powers of x 1.
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