PracticeExam2

# Page 4 math 222 exam 2 c 6 points what is the

This preview shows pages 4–11. Sign up to view the full content.

Page 4

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

View Full Document
Math 222: Exam 2 (c) [6 points] What is the interval of convergence? (d) [2 points] Where does the series converge absolutely? (e) [2 points] Where does the series converge conditionally? Page 5
Math 222: Exam 2 3. (a) [8 points] Estimate the error in using the ﬁrst ﬁve terms of the power series for e x to approximate e . In particular, ﬁnd a rational number greater than the error (you may assume that e < 3). (b) [8 points] Recall that X n =0 ( - 1) n 2 n + 1 = π 4 . How many terms of the series would you use to approximate π to within 1 / 100? Justify your answer. Page 6

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

View Full Document
Math 222: Exam 2 4. [10 points] Set up but do not solve an initial value problem for y ( t ) = pounds of salt in a tank after t minutes. Assume the tank starts with 20 gallons of saltwater at time t = 0 and that each gallon has 1 / 4lb of salt. Pure water is ﬂowing into the tank at a rate of 3 gallons per minute and saltwater is ﬂowing out of the tank at a rate of 4 gallons per minute. Assume the solution in the tank is kept perfectly mixed. Page 7
Math 222: Exam 2 5. Find the general solution to the following diﬀerential equations. (a) [8 points] e y - x dy dx = x . Solve for y ( x ) in your solution. (b) [8 points] xy 0 - 2 y - x 2 = 0 Page 8

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

View Full Document
Math 222: Exam 2 (c) [8 points] y 00 - 6 y 0 + 13 y = 0 6. (a) [4 points] Solve y 00 - y 0 - 2 y = 0. Page 9
Math 222: Exam 2 (b) [8 points] Find a particular solution for y 00 - y 0 - 2 y = 12 e 2 x . Page 10

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

View Full Document
Math 222: Exam 2 (c) [4 points] Solve y 00 - y 0 - 2 y = 12 e 2 x if y (0) = 1 and y 0 (0) = 0. Page 11
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page4 / 11

Page 4 Math 222 Exam 2 c 6 points What is the interval of...

This preview shows document pages 4 - 11. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online