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Unformatted text preview: em. Question 1 [20 points] Determine whether or not the following limit exists. If it exists, what is its
value? (Make sure you justify your answer.)
(x,y )→(0,0) 2x4 + y 4
lim Question 2. [20 points] Suppose that
g (x, y ) = y 2 sin(x + y ),
dt when t = 2. 2
t y = tet . Question 3. [45 points] Consider the function
f (x, y ) = 2xy + y 2 .
(i) Find the directional derivative of f in the direction of the vector 1, −2. (ii) Find the equation of the tangent plane to the surface deﬁned by the equation z = f (x, y ) at the
point (1, 1, 3). (iii) Find the critical points of f and determine whether they are local maxima, minima, or saddles. Question 4 [15 points] The dimensions of a rectangle are 5cm and 10cm, with an error in measurement
of at most 2cm. Use diﬀerentials to calculate the maximum error in computing the area of the rectangle. Quiz 2 – MA 225 B4 – Spring 2011 Instructor: Margaret Beck
Date: March 10, 2011 Name:
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This note was uploaded on 02/13/2014 for the course MA 225 B1 taught by Professor Beck during the Spring '11 term at BU.
- Spring '11