I am having some difficulty with the following problems:
1. For the function
use definition
to determine for which unit vectors
v = v
i + w
j the direction derivative [tex] D_vf(0,0) exists.
I am able to get the function down to the following:
Simplifying I get:
This is where I get lost. The answer is supposed to be v|w|. The limit I have goes to 0.
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Problem 2
The depth of a lake is given by
find the direction a swimmer should swim so that there is no change in the depth. The swimmer begins at (1,-2).
This is part 2 of the problem. Part one has me find the direction the depth increases most rapidly and I got
To be honest I am not quite sure where to begin. Would I set the gradient equal to zero at that point and go from there?
Thanks for any and all help.