 # Problem 1: Consider the function f(x,y)=2x²in(y)-3x²y = a...

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Problem 1: Consider the function f(x,y)=2x²in(y)-3x²y = at the point (a, b, f(a,b))=(1,1,f(l,1)). (a) Find fy (x,y), , fy y (a,b). , and f(a,b). (b) Give a vector tangent to the surface at the point, and in the direction of the y axis. Then, write the equation of the tangent line that has that vector as its direction vector. (c) Give a vector tangent to the surface at the point, and in the direction of the X axis. Then, write the equation of the tangent line that has that vector as its direction vector. (d) Give a vector normal to the surface at the point. Then, write the equation of the tangent plane that has that vector as its normal. (e) Produce an Octave plot of the surface, the two tangent lines, and the tangent plane. Recommend setting up mesh from 0 to 2 for both X and y. That will center the plot around the point of interest at (1,1), and avoid the regrettable side effects of "log of negative number."

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