MAC 2313 Midterm: MAC 2313 FIU Exam 218k
15 Feb 2019
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Prof. s. hudson: [15pts] let r(t) = h3 sin(t), 3 cos(t), 4ti. Then, nd the equation of the osculating plane: [5 pts each] 2a) suppose t (x, y) = xy is the temperature at (x, y) on a thin plate which occupies the rst quadrant of the plane. Sketch the level curves (the isothermal curves) where t = 2 and t = 3. 2b) give an example of a function f (x, y) such that fx(0, 0) = fy(0, 0) = 0, which is not continuous at (0, 0). 2c) suppose z = f (x, y) has a local linear approximation (a tangent plane) at the point (3, 2). Suppose the approximation has the equation z = 4(x 3) + 5(y 2) + 6. F (3, 2): let r(t) = ht3 2t, t2 4i. Compute tr(r, ), leaving your answer in terms of r and as usual: let f (x, y, z) = xz ln(xy2 sin(z)).
