Name: Ziqing Yao
Professor: Debbie Good
Due: 22/ Jan 2015
Personal assessment
There is a common fact that nobody is perfect, everyone has their own merits
and demerits , but the key is to understand yourself and find our your
weakness and strength which a
Qing dynasty was not collapsed in one day. The depression of the economic, a
chaos of political and the corruption of the government make China getting worse and
worse. Britain began to sell drug to China in order to gain a huge profits. The drug
smugglin
Please discuss how Martha Nussbaums ideas about empathy, disgust, a capability
approach, and social justice in Literature, Empathy, and the Moral Imagination
apply to some of the material we have discussed over the course of the semester, in
Units 1, 2, a
Ethics &Stakeholder MGT( HW 1)
Name: Ziqing Yao
Professor: Paul M. Klein
For me, the top ten values are listed as: Effectiveness, Creativity, Honesty,
ambition, intelligence, kindness, respect, persistence, teamwork, courage. I selected
five of them and o
(situational values hypothesis): The choice of an ethical principle de-pends on the
values demanded by the situation. The principles of utilitarianism will be activated in
situations in which universalistic values motivate self-transcendentactions. Reacti
S corporation vs. C corporation: The similarities
The C corporation is the standard corporation, while the S corporation has elected a
special tax status with the IRS. It gets its name because it is defined in Subchapter S of
the Internal Revenue Code. To
Defn: The derivative of a function
at a number , denoted by lim
, is
if this limit exists. Alternate fom of definition of derivative: lim
20.
The limit
lim and . to see that , determine
represents the derivative of some function
at some
number . Determine
The Derivative as a Function Recall that lim gives the derivative of a function at the point But we saw that, given , that . This is evaluated to give the derivative's value for any number replacing . But it could also be considered a function (of ). Now
Derivatives of Polynomial & Exponential Functions
Given a constant function lim Given the function lim Given the function Since lim lim Given the function Since , lim lim lim lim , its derivative . lim lim , its derivative lim . lim .
, its derivative lim
The product rule If Proof:
lim
and
are differentiable functions, then lim
lim lim lim
lim lim lim
lim lim
lim lim
lim lim
The Quotient rule If and are differentiable functions, then
MTH 173 ection 3.2 notes page1
4.
differentiate
Note that:
product rule
8
Rates of Change Recall that And then and the average rate of change of And the instantaneous rate of change of (of ) with respect to with respect to lim 208-2 A particle moves according to a. Determine the velocity at time Since b. the rate of change of p
Derivatives of the Trig Functions Consider lim sin
There are several ways to determine the value of this indeterminate limit One way is to graph both sin and on the same plane: as , how do the graphs compare? a zoomed in graph is below
Another way is to g
The Chain Rule
The Chain Rule says that if , then
Sometimes we say: Given and , then
So, in Here we decompose the function into two functions and , which are
then, with we have
and and
so that
2.
decompose some function, where some function ,
so that then
Implicit differentation
Consider the equation The graph is below. This equation is not a function.
A point on the curve is . Does the curve have slope there? Does it have a tangent line there?
If we just look at the graph "near"
, it is a function - see b
Since
ln
log
we can differentiate
wrt ln
to obtain
more generally, we have log because log
ln
ln
ln
ln
ln
ln
The chain rule version for ln example: ln or we can rewrite given ln ln what is as ln
ln is
ln ?
recall that
so that then
ln ln
ln ln
so that
ln
c
4.
If
and
, determine
differentiate implicitly wrt time
when at and at
then , we have , we have
, so
8. If a snowball melts so that its surface area decreases at a rate of cm /min, determine the rate at which the diameter decreases when the diameter is 10
We know that, given a differentiable function , that the line tangent to the curve at
, and a point on the graph has slope and equation
If is "sufficiently close" to , then we can use points on the tangent line as approximations to . In this sense, the ta
Absolute and local minimum and maximum values Defn: A function has an absolute maximum at if domain of . The number is called the maximum value of A function has an absolute minimum at if . The number is called the minimum value of The maximum and minimum
antiderivatives
Determining antiderivatives or indefinite integrals is essentially "undoing differentiation." When we are to determine the antiderivative of , we are to find the functions such that . The basic integration rules on the top half of referenc
The Mean Value Theorem Consider: Let be a function that is: 1. continuous on the closed interval 2. differentiable on the open interval 3.
Rolle's Theorem Let be a function that is: 1. continuous on the closed interval 2. differentiable on the open interv
Definition A function 0 is increasing on an interval if for any two numbers B" and B# in the interval, B" B# implies 0 aB" b 0 aB# b. A function 0 is decreasing on an interval if for any two numbers B" and B# in the interval, B" B# implies 0 aB" b 0 aB# b
MTH 174, section 4.4 Recall that, given , the tangent line to the graph at has equation
^ Thm L'Hopital's rule Let and be functions that are differentiable on an open interval containing , except possibly at itself. Assume that for all near except possibl
Summary of Curve Sketching
we look for these: domain intercepts symmetry or periodic behavior increase/decrease max/min concavity then use these to sketch the graph 6. C oe BaB #b$ all reals as is polynomial Boe!Coe! C oe ! B oe ! # none
domain: intercept
8.
cardboard
ft maximize volume
base
side
x
cut out squares feet on a side. by by
x
dimensions of box are so volume is
Since all dimensions must be positive, we know that . Thus we are to maximize in this interval. At the end points, we have we determine
Areas & Distances
The area problem:
What's the area of the shaded region:
We can approximate the area with a set of rectangles. The more rectangles, the better the approximation. These four give a very rough approximation:
These eight give a better approx
The Definite Integral in this section we define the definite integral and learn some ways to evaluate it using the summation formulas below and using areas of geometric figures. Summation Formulas 1. 2.
3.
4.
Example:
Example: lim
lim
lim lim Example:
lim