Johns Hopkins University, Department of Mathematics
Calc III Spring 2012
Final Exam
Instructions: This exam has 5 pages and is out of 80 points. No calculators,
sure to show all work for all problems. No credit will be given for answers with
not have e
PILOT
Calculus III
Spring 2013
Problem Set 4
1. Show that Newtons potential V = GmM/r satisfies Laplaces equation
2 2 2
+
+
= 0 for (, , ) (0,0,0).
2 2 2
2. Determine the second-order Taylor formula for the given function about the given point (x 0 , y
PILOT
Calculus III
Spring 2013
Problem Set 1
1. An airplane is located at position (3, 4, 5) at noon and traveling with velocity 400i + 500j k kilometers per hour.
The pilot spots an airport at position (23, 29, 0).
a. At what time will the plane pass dir
PILOT
Calculus III
Spring 2013
Problem Set 2
1. Compute the following limits:
a). lim ( 2 3 + 5)
3
b). lim sin
0
( + )2 2
0
c). lim
2. Let ( , ) = (2+3) .
a. Find the tangent plane to f at (0,0).
b. Use this to approximate f (0.1, 0) and f (0, 0.1).
c. W
PILOT
Calculus III
Spring 2013
Problem Set 3
a).
b).
c).
( , , ) = 2 2 + 2 + 2
( , , ) = 2
( , , ) =
1. Describe some appropriate level surfaces and sections of the graphs of
2. Let (, )and = (, , ), = ( , , ) be given (differentiable) real-valued func
Department of Mathematics
Johns Hopkins University
110.202 Calculus III
Course Syllabus
The following list of topics is considered the core content for the course 110.202 Calculus III.
The current text for the course is:
Text: Vector Calculus, 6th Edition