# Past Exam for MATH 022 - Calculus II for Physical Sciences and Engineering at UC-Merced (UC Merced)

## Exam Information

 Material Type: Final Professor: Staff Class: MATH 022 - Calculus II for Physical Sciences and Engineering Subject: Mathematics University: University of California-Merced Term: Fall Semester 2007 Keywords: Problem ScoreCalculatorsExtra CreditDecompositionEngineering

## Sample Document Text

Name:_______________________ SID:_______________________ Section:_______________________ Final Exam -Math 022-F '07 The exam is 3 hours long. No calculators or notes are permitted. Show your work. You do not need to simplify your answers. Problem Score out of 10 1 2 3 4 5 6 7 8 9 Extra Credit Total Out of 90 1. It is a fact that ? ? n=1 1 n2 = pi2 6 . How well does 20 ? n=1 1 n2 approximate pi2 6 ? 2. Sketchthepolarcurve r = sin(2?)onthecoordinateaxesgivenbelow. Find the area of one "leaf". x K1.5 K1.0 K0.5 0 0.5 1.0 1.5 y K1.5 K1.0 K0.5 0.5 1.0 1.5 3. Find the area of the finite region bounded by the curves y = x2, y = (x?2)2, and y = 0. For the follow two problems, determine whether the series converges. Explain your reasoning for both. 4. ? ? n=1 e?n22 5. ? ? n=1 parenleftbigg1 n parenrightbiggn 6. In the coordinate axes ...