{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# fin - Calculus II V1102 Section 007 Fall 2007 Final Exam...

This preview shows pages 1–5. Sign up to view the full content.

Calculus II V1102 Section 007, Fall 2007 Final Exam Thomas D. Peters Name: December 18, 2007 Do all problems, in any order. Show your work. An answer alone may not receive full credit. No notes, texts, or calculators may be used on this exam. Problem Possible Points Points Earned 1 8 2 13 3 9 4 5 5 4 6 6 7 5 8 5 9 5 10 9 11 6 TOTAL 75 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
1. (a)(4 pts) Compute e 2 x e 2 x + 1 dx (b)(4 pts) Compute e x e 2 x + 1 dx 2
2. In this problem we find the exact value of S = n =0 ( - 1) n 3 n + 1 (a)(2 pts) Explain why S converges. (b)(3 pts) Show that S = 1 0 dt 1 + t 3 by expanding the integrand as a series and integrating term by term. (c)(3 pts) Use partial fractions to decompose 1 t 3 + 1 (d)(5 pts) Use your answer from (c) to compute 1 0 dt 1 + t 3 . 3

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
3. True or false. You MUST explain your answer (a)(3 pts) If { a n } and { b n } are divergent sequences then { a n b n } is also a divergent sequence. (b)(3 pts) If a n converges and a n > 0 for all n then a n is eventually decreasing.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}