1
Properties of limits
1. Let f, g be two functions with lim f (x) = 2 and lim g(x) = 6. Showing all your steps,
xc
xc
simplify the following limits.
(a) lim[8g(x)]
xc
lim[8g(x)] = 8 lim g(x) = 8 6 =
MTH 201
Chapter 6: Application of Integration
Spring 2016
6.4 Length of a Plane Curve
General Idea:
Determine the length of the following curves:
Here the length of the curve is easy to calculate.
Her
MTH 201
Chapter 6: Application of Integration
Spring 2016
6.3 Volumes By Cylindrical Shells
In 6.2 we found that we could compute the volumes of solids or revolution using the washer and disk methods.
MTH 201
Chapter 6: Application of Integration
Spring 2016
6.2&6.3 Volumes Worksheet
1. Let be the finite region bounded by the graphs of = ln() , = 3, = 5, & = 0. Set up a definite
integral which repr
MTH 201
Chapter 6: Application of Integration
Spring 2016
6.1 Areas Between Curves
A Quick Review:
Example:
Let be the area of the region that lies above the -axis and under the graph of = 2 between =
MTH 201
Chapter 6: Application of Integration
Spring 2016
6.5 Area of a Surface of Revolution
General Idea:
When a curve is revolved to form a solid we can try to determine the resulting solids latera
MTH 201
Chapter 6: Application of Integration
Spring 2016
6.2 Volumes of Revolutions (Disk & Washer Method)
General Idea:
In this section we are interested in trying to use our knowledge about integra
Math 180: Calculus I
Fall 2014
September 11
TA: Brian Powers
Example 4.1 Is the following function continuous at a?
1. f (x) =
2x2 +3x+1
x2 +5x ; a
2. f (x) =
x2 1
x1
3
=5
if x 6= 1
;a = 1
if x = 1
1.
Math 180: Calculus I
Fall 2014
October 14
TA: Brian Powers
1. On the following graph to determine at what x values on the interval [a, b] local and absolute extreme
values occur.
SOLUTION: Local minim
Math 180: Calculus I
Fall 2014
October 28
TA: Brian Powers
When graphing functions, there is some basic analysis that will help you do it.
Identify the domain or the interval in question
identify if
Math 180: Calculus I
Fall 2014
November 25
TA: Brian Powers
1. Use symmetry to evaluate these integrals
R /4
(a) /4 cos xdx
SOLUTION: Since the cosine function is an evan function, and the interval is
Math 180: Calculus I
Fall 2014
October 16
TA: Brian Powers
1. Sketch a function that is continuous on (, ) with the following conditions: f 0 (1) is undefined;
f 0 (x) > 0 on (, 1); f 0 (x) < 0 on (1,
Math 180: Calculus I
Fall 2014
October 9
TA: Brian Powers
We may use the following derivative rules now:
d
1
sin1 x =
dx
1 x2
d
1
tan1 x =
dx
1 + x2
d
1
sec1 x =
dx
|x| x2 1
d
1
, for 1 x 1
cos1 x =
Math 180 Week 8 Tuesday
1. Compute the derivative of the following functions.
(a) y = (tan-1x)?
y'= italm - -L
('13
Fall 2015
2. A baseball diamond is in the shape of square. Each side has a length of
1 Computing limits
1. Below are six graphs.
0/ 0/ ./ ./ / /
/ /' /O /
l 2 3 4 5 6
Which of these graphs satisfy the properties below?
(a) the graph is a function
1,2,3,5,6
(b) the graph is dened at ev
MTH 201
Chapter 6: Application of Integration
Spring 2016
6.7 Moments and Centers of Gravity
General Idea
Suppose we have a flat plate (called a lamina) of some material with uniform density which occ
MTH 201
Chapter 6: Application of Integration
Spring 2016
6.1 Areas Between Curves Worksheet
1. Find the area of the region enclosed by the curves = 2 and = 2 2 .
Find Intersections:
2 = 2 2
Setup:
2
MTH 201
Chapter 6: Application of Integration
Spring 2016
6.6 Work
The word work is often interpreted to mean the amount of effort required to perform a task.
When used in the area of physics, the ter
PHY 201.005 Spring 2016
Exam #1
Chapter 1 - 4
Answer the following multiple choice questions. Assume a standard Cartesian coordinate system and
negligible air resistance unless otherwise stated. Selec