Physics 111: Elementary Physics
Laboratory E
Thin Lenses
1.
Introduction
A lens is a transparent object with two refracting surfaces shaped such that it can produce an
image by refracting light that comes from an object. A lens that causes parallel light
5.5
Substitution Rule
Substitution method works whenever we have an integral that we can write in
the form
In the composite function f (g(x) in equation, we identify the inner function
as u = g(x), which implies that du = g(x) dx. Making this identificati
4.7
LHpitals Rule
Some limits, called indeterminate forms, cannot generally be evaluated using the techniques
presented in Chapter 2.
A powerful result called lHpitals Rule enables us to evaluate such limits with relative
ease.
CLASS WORK
convert the diff
5.5
Substitution Rule
Substitution method works whenever we have an integral that we can write in
the form
In the composite function f (g(x) in equation, we identify the inner function
as u = g(x), which implies that du = g(x) dx. Making this identificati
5.5
Substitution Rule
Substitution method works whenever we have an integral that we can write in
the form
In the composite function f (g(x) in equation, we identify the inner function
as u = g(x), which implies that du = g(x) dx. Making this identificati
3.11
Related Rates
The essential feature of related rates problems is that two or more variables,
which are related in a known way, are themselves changing in time.
After the first example, a general procedure is given for solving relatedrate problems.
4.6
Mean Value Theorem
Many of the results of this chapter depend on one central fact, which is
called the Mean Value Theorem.
But to arrive at the Mean Value Theorem we first need the following
result.
Our main use of Rolles Theorem is in proving the fol
3.11
Related Rates
The essential feature of related rates problems is that two or more variables,
which are related in a known way, are themselves changing in time.
After the first example, a general procedure is given for solving relatedrate problems.
Subash Bhandari
[email protected]
PHY 2048 SI
Exam 2 Review
M 4:00-4:50 (GS 222)
W 4:00-4:50 (GS226) & 7:00-7:50 (GS 226)
1. A horizontal 490 N force is exerted on a 100 kg Crate causing it to slide across a level floor at
constant velocity. What is the ma
Experiment #10: Specific Heat Capacities of Metals
Rushawn Ragoonanan
Minxiao Yang
Section: 13
Purpose:
To measure the specific heats of aluminum, steel and brass.
Theory:
The heat required to change an objects temperature (Q) is proportional to the objec
2.3
Techniques for Computing Limits
Limits of Linear Functions
The graph of f (x) = mx + b is a line with slope m and y-intercept b.
Examples: Evaluating Basic Limits
1.lim 3 3
x5
2. lim x
2
(3) 2 9
x 3
3.lim 5 x 5(1)3 5
3
x 1
Example (1 of 2)
Find the f
2.5
Limits at Infinity
In Section 2.4 we investigated infinite limits and vertical asymptotes. There we
let x approach a number and the result was that the values of y became
arbitrarily large (positive or negative).
In this section we let x become arbitr
5.3
Fundamental Theorem of
Calculus
The Fundamental Theorem of Calculus is appropriately named because it
establishes a connection between the two branches of calculus: differential
calculus and integral calculus.
Area Functions
The first part of the Fund
Chapter 5
Integration
5.1
Approximating Areas under
Curves
THE AREA PROBLEM
We begin by attempting to solve the area problem: Find the area of the region S that lies
under the curve f (x) from a to b.
Recall that in defining a tangent we first approximate
2.4
Infinite Limits
Two limit scenarios are frequently encountered in calculus: Infinite limit and limit at infinity.
Infinite limit: function values increase or decrease without bound near a point.
limit at infinity occurs when the independent variable x
4.9
Antiderivatives
A physicist who knows the velocity of a particle might wish to know its position at a
given time.
A biologist who knows the rate at which a bacteria population is increasing might
want to deduce what the size of the population will b
2.6
Continuity
We noticed in Section 2.3 that the limit of a function as x approaches a can often be found
simply by calculating the value of the function at a. Functions with this property are called
continuous at a.
If any item in the continuity checkli
Chapter 2
Limits
Modern calculus was developed in 17th century Europe by Newton and Leibniz,
but the origins of calculus go back at least 2500 years to the ancient Greeks.
It has two major branches, differential calculus (concerning rates of change
and sl