[20] 4. Functions of Several Variables a. Draw the domain of the following function f(x, y) = In(x + y - 2) x²-1 [3] b.

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20 4 Functions Of Several Variables A Draw The Domain Of The Following Function F X Y In X Y 2 X 1 3 B 1 (96.67 KiB) Viewed 33 times

[20] 4. Functions of Several Variables a. Draw the domain of the following function f(x, y) = In(x + y - 2) x²-1 [3] b. Find all of the first order partial derivatives of: 73 f(x, y, z) = 4y² sin³ x-e²y4+: +4y-x¹6 x2 [5] c. Use partial derivatives to find the equation of the plane tangent to the surface described by the following equation: z = ln(2x + y) at the point which projects onto (-1,3) [7] d. Find the directional derivative Df in the indicated direction Df(2,0) where f(x, y) = xey + y and is the unit vector in the direction of = 21 3 [2] e. The bell from Question 3 is struck by an external ringer as shown in the photo below. The surface of the bell is described by the equation f(x, y) = 16-x² - y2. The bell must be struck in a direction exactly perpendicular to its surface. The bell is mounted in a square-sectioned clock tower such that its apex is located at the point (0,0,16). The structural elements of the tower are such that the beam can only be mounted such that its long axis goes through the point (2,2,8). What is the equation of the long axis of the beam? Assume the beam only translates along its long axis - neglect any swing due to the ropes that suspend it. "(c)Tomo.Yun (www.yunphoto.net/en/)"