{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

20b_03f_2e

# 20b_03f_2e - (a dy dx = e x y y(0 = 0(b y ′ t-t y t 2 =...

This preview shows page 1. Sign up to view the full content.

Math 20B Second Midterm 50 points November 20, 2003 Print Name, ID number and Section on your blue book. BOOKS and CALCULATORS are NOT allowed. One sheet of NOTES is allowed. You must show your work to receive credit. 1. (8 points) Which of the following integrals diverge? Remember to give a reason for your answer in each case! (a) integraldisplay 1 0 e sin x dx (b) integraldisplay 1 0 dx x 2. (12 points) Consider the curve given by y ( x ) = ln x for 1 x e . (a) Write down an integral for its length. (b) The curve is rotated about the y -axis. Write down an integral for the surface area. Do NOT evaluate the integrals. 3. (16 points) Solve the differential equations:
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (a) dy dx = e x + y , y (0) = 0. (b) y ′ ( t )-t ( y ( t )) 2 = t (general solution). 4. (8 points) Write down an integral in polar coordinates for the area of the region that lies inside the curve r = 2cos θ and outside the curve r = √ 2. 5. (6 points) Consider the diFerential equation y ′ ( t ) = 1-y 2 . ±ind the limiting behavior of y ( t ) (that is, what is lim t → + ∞ y ( t )) if the initial condition is (a) y (0) = 0 (b) y (0) = 2. You do not need to solve the equation — a clear explanation in a few words will su²ce. END O± EXAM...
View Full 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