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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 ,
dt when t = 4. x = cos t, 4
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
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- Spring '11