Unformatted text preview: D: Score: 1. (out of 20) 2. (out of 20) 3. (out of 45) 4. (out of 15) Total: (out of 100) Instructions: Please write clearly and show all work. No credit will be given if
answers are not justiﬁed. If the problem asks you to use a speciﬁc method in your
solution, please make sure you do so. No credit will be given if another method is
used. The point value of each problem is written in bold at the beginning of each
problem. 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.)
2x2 y 2
(x,y )→(0,0) x4 + 5y 6
lim Question 2. [20 points] Suppose that
g (x, y ) = x2 ex+y ,
Find dg
dt when t = 2. x = cos t, 2
y= .
t Question 3. [45 points] Consider the function
f (x, y ) = x2 + yx + y 2 .
(i) Find the directional derivative of f in the direction of the vector 3, −1. (ii) Find the equation of the tangent plane to the surface deﬁned by the equation z = f (x, y ) at the
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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
 Beck
 Calculus

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