Math 005C Spring 2017
MATH 005B Calculus III (5 cr)
T R 13:15 15:45
David Matthews
Email: [email protected]
Office Hrs: M 16:00 17:30
T R 10:00 12:00
CRN#30696
R 209
Text: Stewart, Calculus 8th
Section 42. The Calculus of Parametric Curves
For 1 5 : Sketch the graph of the following parametric curves by plotting some
points in the indicated domain. Then eliminate the parameter to show that t
Section 41. Moments and Centroids
Find the area, moments about the x and y axes M x and M y , and center of gravity x, y of the
region bounded by the indicated curves. Give a rough sketch of the regio
Section 38. Improper Integrals
Find the following improper integrals, if they converge. Otherwise, state if they diverge to infinity
(or negative infinity), or if they simply diverge. You might want t
Section 40. Hydrostatic Force and Pressure
Find the hydrostatic force experienced by the vertically submerged plate, given the shape and
dimensions of the plate and the water level. The density of wat
Section 39. Arc Length and Surface Area
For 1 to x : Find the arc length of the given curve.
1.
4
f x x 1 2 , x 2, 4.
8
4x
2.
5
f x x 1 3 , x
6
10x
3.
f x lncosx, x 0, .
6
4.
f x lnsecx, x 0, . Expla
MATH PATH 5C
CLASS POLICIES, GUIDELINES and GENERAL INFORMATION
Professor:
Dr. Jude Thaddeus Socrates
Office:
Phone number:
E-contact:
Robbins 322 P
(626) 585-7494
jtsocrates @ pasadena.edu
Consultati
The Calculus of Sequences and Series:
Basic Definitions and Tests
Jude Thaddeus Socrates
Division of Mathematics, Pasadena City College; Revised May, 2011
Infinite Sequences Definitions and Basic Conc
Math 5C Chapter 12 to Chapter 16
Final Review
1
1: Vectors and Analytic Geometry in 3D Space
a: Vectors
How to read and write points in xyz-coordinate.
How to define and write a vector with two poin
Math 5C Extra Credit Problems
Fall 2015
Name:
Date:
Signature:
Instructions:
1. This is an assignment of extra credit problems. In order to obtain full credit, you are required to write
a perfect and
MATH 5C Honors - Test #2 (Chapter 13) Fall 2015
Please show all of your work. Each problem is worth *4points (plusZ'
"free" points). 6 Mi 3 7 l6 1
#1.) Find F(t) and 3(1) if Ei(t)=(2,0,2t) and 17(0)=(
KE/
MATH 5C - Test #1 (Chapter 12) Summer 2013
Please show all of your work.
Spts. #1.) Find the equation of a sphere that passes through the point
(6, -2, 3) and has center (-1, 2, l).
NH)L +c3-zrur(
Section 45. Infinite Sequences
Do the following problems from Stewart, Section 12.1 (Sequences)
5, 7, 17-45 odds, 57, 61-67 odds.
1.
Consider the recursive sequence:
a 1 3, and a n1 3 a n 6.
7
2.
a.
C
Section 47. The Integral Test
Do problems 3-29 (odds) from Stewart, Section 12.3 (The Integral Test)
1.
It is known (but difficult to prove) that
n12
n1
2
converges to 1. 644934068.
6
a.
Show that th
Section 54. Taylor and Maclaurin Series
Do problems 5, 7, 9, 15, 17, 19, 25, 27, 29, 33, 43, 47-67 (odds) from Stewart, Section 12.10
(Taylor and Maclaurin Series)
For 1 6 : Compute an approximate val
MATH 005C Group Work
Do your work on separate paper. You will be working together, but you
are each responsible for your own work.
1. A) Find parametric and symmetric equations for the line that passe
Find the shortest distance between a point and a line in 3 dimensions:
A) Let P = (x0, y0, z0) and define the line, L, not containing P by x = x 1 + a t , y = y1 + b t, z = z1 + c t, with
<a,b,c> a UN
Section 56. Separable Differential Equations
Do problems 1-17 (odds), and 41, from Stewart, Section 10.3 (Separable Equations)
1.
A tank contains 400 liters of salt solution. At the start of the proce
Section 55. Applications and Further Manipulations of Taylor Series
For 1 4 : Find the following limits using infinite series:
1.
2
ln1 x x x
2
lim
3
x0
x
2.
lim
sinx tan 1 x
tanx x
3.
lim
cosx e x x
Section 49. The Alternating Series Test
Do problems 3-19 (odds) and 23, 25 from Stewart, Section 12.5 (Alternating Series)
Section 50. Absolute/Conditional Convergence and the Root and Ratio
Tests
Do
Section 48. The Comparison Tests
Do problems 3-31 (odds) from Stewart, Section 12.4 (Comparison Tests)
1.
The Ordinary Comparison Test is sometimes useful to determine if an infinite series
involving
Section 44. Areas of Regions Bounded by Polar Curves
Find the exact area of the region bounded by the indicated polar curve/s (some of them appeared
in the previous section, and their graphs from the
Section 46. Introduction to Infinite Series
Do problems 9-45 (odds) from Stewart, Section 12.2 (Infinite Series)
The following are all telescoping series. For each of them: (a) find the first 5 partia
Section 43. Tangent Lines to Polar Curves
Sketch the graph of the following polar curves by plotting some points in the indicated domain.
Find the polar coordinates of all the points where the tangent
Section 37. Approximate Integration
For each of the following definite integrals:
(a) approximate the integral using The Trapezoid Method with n 8 subintervals;
(b) approximate the integral using Simp
Section 52. Power Series
Do problems 3-33 (odds) and 41 from Stewart, Section 12.8 (Power Series)
Section 53. Representing Functions with Power Series
Do problems 3-17 (odds), 23-33 odds and 37 from S
KEY
MATH 5C Honors - Test #1 (Chapter 12) Spring 2016
Please show all of your work. Each problem is worth 16 points. This,
plus 4-"free" points totals 100 points.
#1.) Find the angle between a diagona
KEY
5C Honors Final Exam Fall 2015 . :
. Page 1 of 2 I
'puints with 8 free points. Please 141.1211]
" ofthe space curve giVen by ;()=<t2"0?lll I.
-; W, 1:; 0.0558) V I
l L lite.) lef and f if 6ff(x,
KE y
Math 5C Honors - Test #4 - Chapter 15 - Fall 2015
Please show all of your work. Each problem is worth 16 points, plus 4 "free" points.
81. ) Calculate yexydA where R: cfw_(x, y) I 0 S x S 2, 0 S