{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Final Fall 2005

# Final Fall 2005 - Math 122 Final Name 1 2 3 4 5 6 7 8 9 10...

This preview shows pages 1–6. Sign up to view the full content.

Math 122 Final December 13, 2005 Name 1 2 3 4 5 6 7 8 9 10 Total / 200 Directions: 1. No books, notes or passing go and collecting \$200. You may use a cal- culator to do routine arithmetic computations. You may not use your calculator to store notes or formulas. You may not share a calculator with anyone. 2. You should show your work, and explain how you arrived at your an- swers. A correct answer with no work shown (except on problems which are completely trivial) will receive no credit. If you are not sure whether you have written enough, please ask. 3. You may not make more than one attempt at a problem. If you make several attempts, you must indicate which one you want counted, or you will be penalized. 4. You may leave as soon as you are finished, but once you leave the exam, you may not make any changes to your exam.

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

View Full Document
1. (20 points) (a) Z dx e x e 2 x + 4 Hint: Z du u 2 u 2 ± a 2 = u 2 ± a 2 a 2 u + C (b) Z x + 1 3 x 2 + 2 x - 16 dx (c) Z x sec 2 x dx (d) Z sin 3 x cos 3 x dx .
2. (20 points) (a) Z 1 + sin x 1 - sin 2 x dx . (b) Z (sec 3 3 x )(tan 3 3 x ) dx (c) Z 1 - x 2 x 2 + x dx (d) Z 1 (4 + x 2 ) 3 / 2 dx

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

View Full Document
3. (20 points) (a) For the differential equation dy dx = F ( x, y ), where F ( x, y ) is given below: x 0 1 2 3 4 0 1 0 -1 -1 0 1 0 1 0 1 0 y 2 -1 0 -1 1 1 3 -1 1 0 1 0 4 1 1 -1 -1 1 Use Euler’s method with h = 1 and y (0) = 0 to approximate y (4). (b) Find the solution for the following differential equations. i. dy dx = - 4 xy 2 y (0) = 1 ii. dy dx - y = e 2 x y (0) = 3
4. (20 points) A tank contains 30 gallons of pure water. Water containing 2 pounds of Grape Kool-aid mix dissolved per gallon enters the tank at 5 gallons per minute. The well-stirred mixture drains out at 5 gallons per minute. (a) Write a differential equation (with initial condition) for how much Grape Kool-aid mix is in the tank at any time.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern