Question: Prove that is continuous on R2 and has first-order partial derivatives everywhere on R2, but f is not differentiable at (0, 0). (x, y)(0.0) (x,

Prove that
Prove that
is continuous on R2 and has first-order partial derivatives

is continuous on R2 and has first-order partial derivatives everywhere on R2, but f is not differentiable at (0, 0).

(x, y)(0.0) (x, y) = (0,0) f(x, y) = X2 +y2 0

Step by Step Solution

3.37 Rating (172 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Clearly f is continuous and has firstorder partial derivatives at every point x y 0 ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

741-M-N-A-D-I (631).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!