help please with these 5 questions

1. [6 points] Evaluate the improper integral 2 1 (it: L as 2. [5 points} Find the limit of the given sequence [nth term is given] and discuss its convergence! divergence on: 21(1 cos (1)) . OR 2. [5 points] Use partial fractions to simplify the given rational function into a sum/ difference of two simpler rational functions 3+2 323I+2 3: [7 points} Use the integral test to determine Whether the series converges or diverges 1 Z n{ln in.)2 11.22 4. [6 points} Use the Direct Comparison Test OR Limit Comparison Test to deter- mine the convergence! divergence of the series 2 axial n=2 5. [6 points] Discuss whether the series is absolutely convergenticonditionally convergent