a4 - 4 Let f R 2 R and dene g x y = f(sin y cos x Find g xx...

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

View Full Document Right Arrow Icon
Math 237 Assignment 4 Due: Friday, Oct 15th 1. Determine all points where the function is differentiable. a) f ( x, y ) = x 3 + y 3 x 2 + y 2 , if ( x, y ) = (0 , 0) 0 , if ( x, y ) = (0 , 0) . b) g ( x, y ) = | x | 1 / 2 . 2. Prove that if all of the second partial derivative of f are continuous at ( a, b ), then f is continuous at ( a, b ). 3. Let f, g : R R where f and g are twice differentiable. Show that u ( x, t ) = f ( x - at ) + g ( x + at ) is a solution of the wave equation: u tt = a 2 u
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: . 4. Let f : R 2 R and dene g ( x, y ) = f (sin y, cos x ). Find g xx and g yy . State any assumptions you needed to make. 5. Let f ( x, y ) = | x | r | y | s , where r and s are positive numbers. a) For what values of r and s is f dierentiable at (0 , 0)? b) For what values of r and s is f dierentiable on R 2 ?...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern