Workout Problem (60 points) Part a: (20 points) 1. Find the domain of the vector function r(t) =< ln(t + 2), t 1-12 ' 2.

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Workout Problem 60 Points Part A 20 Points 1 Find The Domain Of The Vector Function R T Ln T 2 T 1 12 2 1 (39.91 KiB) Viewed 54 times

Workout Problem (60 points) Part a: (20 points) 1. Find the domain of the vector function r(t) =< ln(t + 2), t 1-12 ' 2. Compute the limit lim r(t), 1-0 r(t) =< te-21, ¹1, cos 2t> Part b: (20 points) We consider the function 21 f(x, y) = x sin y - y cos x + - for * y Find fx(x, y), fxy(x, y), and fxyx(x, y). Part c: (20 points) 1. Find the gradient of the function f(x, y, z) = ln(xy) - zx² at the point (1, 1,-1). 2. Find the directional derivative of the function f(x, y, z) = ln(xy) - zx² at the point (1, 1,-1) in the direction of the vector < 1, −3, 1 >.