I am having some difficulty with the following problems:
1. For the function
use definition to determine for which unit vectors v = vi + wj the direction derivative 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.
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.
For the first problem, in the first problem on this part:
The square root symbol is over the entire line. So, if we factor out then we get in that line. Then shouldn't ? We can then move the h in the very bottom up to the top. I suppose I am not seeing where I am losing an h