H let u h a b i be any unit vector find the

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(h) Let ~ u = h a , b i be any unit vector. Find the directional de- rivative f ~ u ( 0 , 0 ) by filling out and evaluating the limit (simplify your answer as much as possible): f ~ u ( 0 , 0 ) = lim h 0 1 h ( - f ( 0 , 0 )) = (Enter DNE for the limit if it does not exist.) Does this exist for every ~ u ? ? (Be sure that you can justify all of your answers in this prob- lem.) 0
h 2
0 0 0 0 x*yˆ2/(xˆ2 + yˆ2)ˆ(3/2) 1/2ˆ(3/2) no a*bˆ2/(aˆ2 + bˆ2) 0 no hˆ3*a*bˆ2/(hˆ2) a*bˆ2 yes Generated by c WeBWorK, , Mathematical Association of America 3

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