The function f(x, y, z) is defined and smooth at everypoint in 3-space and grad f(1, 7

Chapter 17, Problem 50

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The function f(x, y, z) is defined and smooth at everypoint in 3-space and grad f(1, 7, 2) =i (6)j + k .The curve C is r = (t + 1)2i + 7 cos tj + 2etk .(a) Find an equation of the tangent plane to the levelsurface of f at the point (1, 7, 2).(b) Find the angle between the normal to the levelsurface of f and the tangent to the curve C at(1, 7, 2). (Note: There are two possible angles; givethe smaller one. Your answer should be in radians.)(c) With x, y, z in centimeters, let f be the concentrationof a pollutant in parts per million (ppm) at thepoint (x, y, z). A particle moves along the curve Cwith the given parameterization and t in seconds.Find how fast the concentration is changing at thetime t = 0. Give units with your answer.