Make sure you justify your answer 3 x2 y 2 xy 00 4x4

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Unformatted text preview: s its value? (Make sure you justify your answer.) 3 x2 y 2 (x,y )→(0,0) 4x4 + y 6 lim Question 2. [20 points] Suppose that g (x, y ) = y 2 ex+y , Find dg dt when t = 4. x = cos t, 4 y= . t Question 3. [45 points] Consider the function f (x, y ) = x2 + 3yx + y 2 . (i) Find the directional derivative of f in the direction of the vector ￿2, −3￿. (ii) Find the equation of the tangent plane to the surface defined by the equation z = f (x, y ) at the point (1, 1, 5). (iii) Find the critical points of f and determine whether they are local maxima, minima, or saddles. Question 4 [15 points] A cylindrical can has radius 5cm and height 10cm, with an error in measurement of at most 3cm. Use differentials to calculate the maximum error in computing the volume of the can....
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