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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 p-test. 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
- Squeeze Theorem