epefk - Final Exam Key, 2 hours and 45 minutes April 24,...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Final Exam Key, 2 hours and 45 minutes April 24, 2003 The average was about 60/100 with the lowest scores on the recent material- power series and polar coordinates. Warning - this key was written days after the exam was graded, so I don’t expect too much interest in it, and I haven’t checked it carefully. The basic methods given are all correct. 1) 1 2 R x 4 dx = 32 / 10 = 16 / 5. 2A) From memory, ln(1 + x ) = x- x 2 / 2 + x 3 / 3- . . . . So, ln(2) ≈ 1- 1 / 2 + 1 / 3 = 5 / 6. Since this is a decreasing alternating series, this answer is too big, but the error is less than the next term, 1/4. 2B) ln(2) = R 2 1 dt t ≈ 2- 1 2 · 3 (1 + 4 · 2 3 + 1 / 2) = 25 / 36. Here, for example, y 1 = f ( x 1 ) = f (1 . 5) = 1 / 1 . 5 = 2 / 3. 3a) Set u = tan x and get (tan 3 x ) / 3 + C . 3b) Do IBP twice to get e x ( x 2- 2 x + 2) + C . 3c) This is improper b/c it has an asymptote at x = 2. A graph is recom- mended. So, it should be split in two (this also helps remove the absolute value signs). The first part isvalue signs)....
View Full Document

This note was uploaded on 12/26/2011 for the course MAC 2312 taught by Professor Storfer during the Summer '08 term at FIU.

Page1 / 2

epefk - Final Exam Key, 2 hours and 45 minutes April 24,...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online