- #1
precondition
- 57
- 0
Determined to finish off my assignment!
Firstly, it's 2:50 am here and I'm NOT going to sleep until I finish this assignment off! I have few remaining ones and I'd be glad if someone could help me out so I can go to sleep...
Please consider this question(and the one I posted below);
f:R^2-->R is defined by f(x,y)=lxyl where lxyl is absolute value of xy
(a)Show that f is differentiable at (0,0)
For this, I think using definition of 'differentiable' is almost impossible, so I'm thinking should I use the theorem which says the function is differentiable if all of partial derivatives exist, and each entry in jacobian matrix exists in a neighbourhood of the point and continuous at that point.
But... partial derivative of something inside absolute value?... also to show each entry in jacobian is continuous... do i use epsilon delta argument??
(b)Show that there is no disc B((0,0);delta) throughout which f has all of its directional derivatives
This one scares me off...
Firstly, it's 2:50 am here and I'm NOT going to sleep until I finish this assignment off! I have few remaining ones and I'd be glad if someone could help me out so I can go to sleep...
Please consider this question(and the one I posted below);
f:R^2-->R is defined by f(x,y)=lxyl where lxyl is absolute value of xy
(a)Show that f is differentiable at (0,0)
For this, I think using definition of 'differentiable' is almost impossible, so I'm thinking should I use the theorem which says the function is differentiable if all of partial derivatives exist, and each entry in jacobian matrix exists in a neighbourhood of the point and continuous at that point.
But... partial derivative of something inside absolute value?... also to show each entry in jacobian is continuous... do i use epsilon delta argument??
(b)Show that there is no disc B((0,0);delta) throughout which f has all of its directional derivatives
This one scares me off...