Math 133, Practice Questions on Sequence and Series
1.(a) Let (1n = for n _>_ 2. Find lim an.
n 1n n nwo
(1)) Let (i.n = (111703 for n 2 2. Find an.
n 2
(0) Let 0n = for n 2 2. Find lim an
n TL 1 nmo
00
((1) Determine whether the series
Math 133, Test 3, 15 November 2012
Name: 3 Ms- QNX .3ng
Instructions. Do each of the following questions. You must show all appropriate details in
your solutions. You may use a scientic nongraphing calculator. Please write nal answers in
spaces provided
Math 133, Test 3, 15 November 2012
Name:
Instructions. Do each of the following questions. You must show all appropriate details in
your solutions. You may use a scientic nongraphing calculator. Please write nal answers in
spaces provided. Good luck.
1. (
Partial Derivatives
Math 133
La Sierra University
December 3, 2012
Partial Derivatives
Given a function z = f (x, y ), we dene
f
f (x + x, y ) f (x, y )
= lim
x0
x
x
and
f (x, y + y ) f (x, y )
f
= lim
y 0
y
y
if the limits exist.
Partial Derivatives and
Cross Products
Math 133
La Sierra University
November 6, 2012
Examples using Cross Products
Example. Compute the cross v u for u = 1, 4, 1 and
v = 2, 3, 0
vu=
i
j
2
3
1 4
= 3, 2, 11
k
0
1
Area of Parallelograms
Example. Find the area of a parallelogram wi
Math 133, Test 2, 1 November 2012
Name:
Hints and Answers
Instructions. Do each of the following questions. Each problem is worth 5pts. You must
show all appropriate details in your solutions. Please write nal answers in spaces provided.
Good luck.
1. A p
Math 133, Test 2, 1 November 2012
Name:
Instructions. Do each of the following questions. Each problem is worth 5pts. You must
show all appropriate details in your solutions. Please write nal answers in spaces provided.
Good luck.
1. A parabola has equati
Math 133, Test 1, 16 October 2012
Name:
Instructions. Do each of the following questions. Each problem is worth 5pts. You must
show all appropriate details in your solutions. Please write nal answers in spaces provided.
Good luck.
1.(a) Find the limit of
Taylor Polynomials
Math 133
La Sierra University
October 3, 2012
Maclaurin Polynomials for Sine
A graph of y = sin x is given.
Maclaurin Polynomials for Sine
Graphs of y = sin x, and y = 0
Maclaurin Polynomials for Sine
Graphs of y = sin x, and y = x
Macl
Math 133, Practice Questions on Sequence and Series
1
for n 2. Find lim an .
n
n ln n
n
(b) Let an =
for n 2. Find lim an .
n
(ln n)3
1.(a) Let an =
(c) Let an =
1 n2
for n 2. Find lim an
n
n n1
(d) Determine whether the series
an where an is as in (a), (
Math 133
Chapter 11 Practice Questions
1. A plane is ying with a bearing of 302 (measured clockwise from north). Its speed with
respect to the air is 900 kilometers per hour. The wind at the planes altitude is from the
southwest at 100 kilometers per hour
Math 133
Chapter 11 Practice Questions with Hints and Rough Answers
1. A plane is ying with a bearing of 302 (measured clockwise from north). Its speed with
respect to the air is 900 kilometers per hour. The wind at the planes altitude is from the
southwe
Math 133, Practice for Test 2 - Hints and Answers
1. Write the equation of the conic x2 + 6x 8y 23 = 0 in standard form, and then nd
its vertex, focus and the equation of its directrix. (Think about similar equations for ellipses
and hyperbolas where you
Math 133, Practice Problems: Conics, Parametric Equations and Polar Coordinates
The following questions are collected from some practice problems suggested to Math 122
students when they study conics, polar coordinates and parametric equations.
1. Write t