MATH 215 Final: finalw05sol
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Express your answer in terms of a unit vector. The gradient of f at the point p is the vector h 1 , 8i. Its direction is the direction of greatest increase, so the direction expressed as a unit vector is. 65 h 1 , 8i. (cid:3) (b) suppose ~r(t) = hx(t) , y(t)i is a parametric curve such that ~r(0) = h2 , 1i, and d. Find the value of dt ~r(0) = h3, 5i. d dt f (x(t) , y(t))|t=0. At t = 0 this is the dot product h3, 5i h 1 , 8i = 37 f (x(t) , y(t)) = dx dt d dt dy dt. Y d~r dt f. (cid:3) (8+7=15 points) suppose that, in an experiment, the temperature of a sample (in. Note that t (0, 1, 2) = 20 , One computes that, at the point (0, 1, 2), the partial derivatives of t are: tx = 2,
