Problem Set #2
MAC 2313 - Summer 2011
12.1
78. The vector-valued function in question is r(t) = 2et i + et j +ln(t 1)k The x-component
and y -component are continuous for all real numbers since
lim 2et = 2ea = x(t) and
ta
lim et = ea = y (t)
ta
for all a
Problem Set #3
MAC 2313 - Summer 2011
13.1
18. f (x, y ) =
Domain:
Range:
4 x2 4y 2
x2
+ y 2 1
4
R = cfw_z |0 z 2
D = cfw_(x, y )|
Note: Since x2 + 4y 2 0, the largest possible value of z =
4 x2 4y 2 is z =
4 0 = 2.
78. Let the constant C is the value of
Problem Set #4
MAC 2313 - Summer 2011
13.6
22.
g (x, y ) =
=
g (2, 0) =
y
2ey/x + 2x 2 ey/x , 2ey/x
x
y y/x
y/x
2e 2 e , 2ey/x
x
2, 2
75. (bonus)
a)
b) The model would give the graph of the ocean oor if we took D.
c) D(1, 0.5) 315meters
d)
fx (x, y ) = 60
Problem Set #5
MAC 2313 - Summer 2011
14.3
24.
/2
5
er
f (x, y )dA =
/2
R
2 /2
rdrd; Let u = r2 /2, du = rdr
0
/2
r=5
eu dud
=
/2
/2
r=0
1 e25/2 d
=
/2
=
1 e25/2
+
2
2
= 1 e25/2
14.4
16. Note that there should be an additional bound of y = 0 in order f
Calculus 3: MAC 2313
CRN 50354 - Summer 2011 (4 credits)
Instructor: Dr. Daniel Kern, Dept of Chemistry and Mathematics, FGCU
Oce: AB7 224
Phone: (239) 590-1261
email: dkern@fgcu.edu
Oce Hours: MWF 11:00-12:00 or by appointment (open door policy)
Text: Ca
STUDY GUIDE
EXAM 1
Go to Study Guide for Exam 2
Go to Study Guide for Final Exam
The first exam covers material from sections 11.1-11.6, and 12.1-12.5. Excluded:
Area of a parallelogram and volume of a parallelepiped (11.4)
Sketching quadric surfaces - bu
STUDY GUIDE
Go to Study Guide for Exam 1
Go to Study Guide for Final Exam
This exam will cover material from sections 13.1-13.10. Anything not covered in class or given for
homework will not be on the exam. Also excluded:
Continuity of composite functions