Let .

1)Determine the domain of .

2)Tell whether exists or not.

3)Calculate via the definition .

4)Determine the equation of the tangent plane of in the point .

5)Determine the equation of the tangent line to the level curve in .

6)Calculate the directional derivative of in the point in the direction .

My attempt :

1) .

2) .

, thus the limit does not exist.

3) evaluated in . This equals .

4) .

.

.

Hence the equation of the tangent plane is .

5) I don't know how to start it.

6) Idem.

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I'd like to check my results and for part 5) and 6) a little push in the right direction.