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Unformatted text preview: Three of the following questions will serve as problems on the final exam: 1. Formulate the definition of lim n a n 2. Formulate the definition of lim x a f ( x ) 3. Prove that if lim n  a n  = 0, then lim n a n = 0. 4. Formulate the squeeze theorem for sequences. 5. Formulate the monotonic sequence theorem. 6. Write the formula for the sum of geometric series. 7. Prove that if the series n =1 a n is convergent, then lim n a n = 0. 8. Formulate the test for divergence. 9. Formulate the integral test. 10. Formulate the ptest. 11. Formulate the comparison test. 12. Formulate the limit comparison test. 13. Formulate the alternating series test. 14. Prove that if a series is absolutely convergent, then it is convergent. 15. Formulate the ratio test. 16. Write the Taylor formula. 17. Write the Maclaurin series for e x . 18. Write the Maclaurin series for sin x . 19. Write the Maclaurin series for cos x . 20. Write the Maclaurin series for ln(1 + x ).  21. Given vector ~ a = h a 1 ,a 2 ,a 3 i , what is its magnitude? 22. Let be the angle between vectors ~ a and ~ b . What is ~ a ~ b ?...
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 Fall '09
 Staf
 Squeeze Theorem

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