Analysis 1 Sample Final - Analysis I section 5 SAMPLE Final...

This preview shows page 1 - 9 out of 9 pages.

Analysis I, section 5 - SAMPLE Final Exam (12/10/2013) [100 marks]Name:Please justify all your answers, unless otherwise instructed. No calculators allowed.Duration: 100 minutes.1. Provide precise definition for the following objects (3 marks each):
Convergence of general Riemann sums
2. Formulate the following theorems precisely (you do not have to prove them! 5 marks each)Sequential Characterization of limits of real functionsCharacterization of uniform continuity on a bounded open intervalTaylor’s TheoremFirst mean value theorem for integralsComparison test for series w/ non-negative terms
3. State the theorem called Root test and prove it. (15 marks)
4. Decide which of the following statements are true and which are false. Prove the true ones and give counterex-

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture