A. Lines
Parametric Eq. of a Line: x = x1 + a(t) , y = y1 + b(t) , z = z1 + c(t)
Symmetric Eq. of a Line: x x1 = y y1 = z z1
a
b
c
1. Find line L that passes through point (x1,y1,z1) & is parallel to
MATH 420 FINAL EXAM DECEMBER 2013 PROF. CAGINALP
No books, notes, calculators, etc. Explain all of your reasoning.
Each problem is worth 20 points.
1. Explain how the exponential and logarithm functio
Solutions. MATH 0420 EXAM 2 NOVEMBER 22, 2013
No books, notes, etc. Explain all reasoning.
1. (20 points) Using the limit definition of derivative prove that
d 5x 2 3 10x.
dx
You can use basic theorem
MATH 0420 info for the nal exam
Kiumars Kaveh
December 5, 2014
The nal is accumulative but the emphasis is more on Chapter 5 and
Sections 6.1 and 6.2.
There will be 5-6 questions in the test.
You a
SOLUTIONS MATH 420 EXAM 2 NOVEMBER 5, 2012 PROF. CAGINALP
No books, notes, calculators, etc. Write all of your reasoning.
1. Show that the function
fx :
x 2 sin
1
x2
if x 0
if x 0
0
has the following
MATH 0420 info for midterm 2
Kiumars Kaveh
November 12, 2014
The midterm covers: Sections 3.5, 4.1-4.4 and 5.1-5.2
There will be 4-5 questions in the test.
The emphasis of the test is on Chapters 4
Math 0420 Homework 3
Guoqing Liu
September 23, 2012
Exercise 3.3.1 Find an example of a discontinuous function f : [0, 1] R where the
intermediate value theorem fails.
Solution: Dene the following fun
Calc 3 F2013, Optimization
Optimization
Critical points, local max/min, Lagrange multipliers, absolute max/min
Types of problems
There are 3 types of optimization problems in Calc 3, and they require
Lon Capa basics
Logging in
Lon Capa can be accessed from any computer with internet connection.
Go to http:/homework.math.pitt.edu/ or http:/homework.phyast.pitt.edu/ (you can also
Google Lon Capa Pit
Calculus 3 Quiz 3 (25 min) NAME:
Problem 1. Find parametric equations of the tangent line to r(t) = (sin(3t),cos(3t),et) at the
point (0, —1,e7'/3).
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r M? 1 3a,; 2M, 32-» e * >
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Calculus 3 Quiz 2 (25 min) NAME:
Problem 1. Find the plane through the points P(1,1,1)J Q(1,2,3), R(0, 1,0).
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'1 W W P/ahe and q we W/ Vtm‘ﬁﬂ-‘s
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Calculus 3 Quiz 1 (20 min) NAME:
Problem 1. Find two unit vectors orthogonal to both i+j + k and 2i + k.
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,4 m a
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Calc 3 F2013, Flux integrals
Flux integrals
Flux integral is an integral of a vector eld over a surface.
F dS =
S
F (ru rv ) dA
D
General strategy
First determine how many dierent surfaces are there,
Department of Mathematics
University of Pittsburgh
MATH 0420 (Theoretical Calculus)
Midterm 1, Fall 2014
Instructor: Kiumars Kaveh
Last Name:
Student Number:
First Name:
TIME ALLOWED: 75 MINUTES. TOTA