quiz_08-key

# quiz_08-key - Exam Course Duration Due Date Instructor 16s...

• Test Prep
• 4

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

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

Unformatted text preview: Exam Course Duration Due Date Instructor : : : : : 16s MATH 2451 quiz 08 Multivariable Calculus 25 min 2016-03-09 (Wed) McCary T.C. Use (First Name) (Last Name) 2016-03-09 09:22 1. (10 points) Determine if each of the following functions is a parametrization of a manifold. � � t √ . (a) γ1 : (−1, 1) → M given by γ1 (t) = 1 − t2 � � cos(π t) . (b) γ2 : (−1/2, 1/2) → M given by γ2 (t) = − sin(π t3 ) �� � x 2. (10 points) Let Xc = y � � � 3 � x + y 3 − 3 y = c . Determine all values of c which make Xc a smooth curve. � 3. (10 points) (a) Several level sets of a function with signature R2 → R are plotted. For each plotted level set, determine if it is a smooth manifold. ��� � � ��� ��� � ��� � � ��� �� �� ���� �� ���� �� �� � � � (b) Several level sets of a function with signature R2 → R are plotted. For each plotted level set, determine if it is a smooth manifold. � ��� ���� � ��� � ���� ���� � �� �� � � ��� ���� ���� �� ���� �� �� � � � �� �� � � � (c) Is the following a smooth manifold? State your reasons. ��� � ��� � ���� �� ���� ...
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