TEST 12_ENGLISH 2_MATHEMATIC NR ‘07

I know.... Being a teacher is Not Easy

On Tuesday, 30 December 2008 as English lecturer teachers are attending the inauguration of the Yogyakarta State University, studying the English replaced day Wednesday. When I was working on a task to take advantage of the English language with a friend named Titin M. I explain to my friends on the Variation of Parameters in the building FMIPA. At 11:15 am, I start explaining about the lessons of differential equation.

Before I recount events funny when I explain about the Variation of Parameters to my friends, I will defining to you, what the Variation of Parameters? We as students of mathematics certainly not foreign to the lessons are. In my opinion, Variation of Parameters is a method to complete differential equation a constant coefficient and variable coefficients which complementary known function. Then we replace any constant c₁ and c₂ on the complementary function (y_c) with the v₁ and v₂ (y_p) so, the solution is a general equation y = y_c + y_p. Differential settlement with the method of variation of the parameters, we need to know the steps. The steps to complete the differential with a variation of parameters, among others: first we write the no homogenous differential equation, both of us to write a corresponding homogeneous equation, is derived from the equation complementary function, and any constant c₁ and c₂ (y_c) from the complementary we replace with v₁ and v₂ (y_p). Y_p function of our lower, further we get a system with variable v'₁ equality and v'₂. Now we find v'₁ and v'₂ with determinant’s coefficient-coefficient equation system it. Once we get v'₁ and v'₂, we seek v₁ and v₂ with integral v'₁ and v'₂. And the last step we substituting v₁ and v₂ on y_p, so we have the general solution of the differential equation.

We do not see a faint first step of a settlement before we try differential. So, yesterday I try to explain the variation of parameters to my friends. Do you want to know the story of my time explaining the variations of parameters to my friends? And this story...

Before the variation of parameters to her, I have to know that my friend was already understood about the lesson before the variation of parameters. Titin already understand the lesson before, so I started explaining the form of differential equation to be completed with the method of variation of parameter. Next, I explain the steps to get a general solution of the equation differential. After I finished the variation of parameters to my friends, whether he understands that it is? Titin equality can do to step down differential y_p function, and then he began to upset the value v'₁ and v'₂. I have to repeat the explanation for the value v'₁ and v'₂. Because it is still not understand, I explained that with the Indonesian language. Successful! She can find value v'₁ and v'₂, now he must integral value v'₁ and v'₂ to get value v₁ and v₂. Usually v'₁ value and the load v'₂ trig functions, so that he has difficulty integral functions. I told him to remember the lessons back integral calculus, so I help him to get value v₁ and v₂. The last step he can finish their own, then I give a problem to him to know what he is familiar or not. With these steps, he can do the problems easily. So, I can conclude that explain things to other people is not easy. We need patience so that we can be successful destination. I know ... being a teacher is not easy, but if we have any intention, we can do so easily.

TEST 11_ENGLISH 2_MATHEMATIC NR ‘07

Blog Opens Window World

In the era of globalization is the development of information rapidly growing virtual world. The internet there is a lot of users. We, the users benefit from internet services to the very existence of the development. We can find the tasks of lecturers easily. We just type the subject matter on the site Google, yahoo, msn, Plaza, hotmail and others, and then we immediately get what we will be looking for. With the development of the information we can easily deal with friends, relatives, teachers, teachers, and others.

The development of information through the web site influence on education. We can find information on various universities across the world with very easily. We can also find a variety of scholarships through various Web sites. Many universities around the world inform universitasnya through the blog. According to Enda Nasution (Mr. Blogger Indonesia), said that since the beginning of the number of bloggers only amounted to tens can know each other from one another, has now developed into 350,000 people. This is the glory with the rapid development of the blogs in Indonesia. Many appear blogger community in Indonesia as Batagor and BBV (Bandung), Cahandong (Yogyakarta), Leonpia (Semarang), mathematics community, and others

Attendance communities’ blog will stimulate the use of a maximum blog. With the development of the community, we can exchange information and get feedback for the improvement we blog. According Dr.Marsigit, with the blog we can communicate with friends, teachers, co-workers, teachers, and we easily get information from university in the world with very easily. We can also participate in the race, race through the blog. With the blog, we can write many scientific papers, books, opinions or ideas.

In Indonesia is very easy to access internet services than in other countries. On 23 December 2008, my lecturer called Dr.Marsigit tells about the experience in Australia. He said that access the internet services in Australia requires a very expensive cost. And an internet service in Australia is only a little. I think, in internet service is cheaper and where there are certain. We are lucky to live in Indonesia, because we can obtain information easily and cheaper. And also the blog, we can know the ideas of experts on various fields of life.

Blogs have many benefits for us, according to Warmoko have some type of useful blogs, among others: the first is the knowledge sharing, this blog is very useful for us because in this blog contains knowledge-knowledge that is useful for many people. Benefits blog is the second bridge blogging, this blog is written in English. We can also learn to write the English language on this blog. On this blog will actually display on the face of a State. Third is the ground voice, "the grassroots voice", on this blog, we can write our opinions and we can see people's ideas about various aspects of life in the world. And the benefits that last idea are incubation. Thus, we can stimulant that make it easier for the blog we have a variety of information in the world.

TEST 10_ENGLISH 2_MATHEMATIC NR '07

Intensive Language via Blog

In my opinion, language is a system of symbols that noise generated by means of human voice and can be used to communicate with fellow human beings, to work together with fellow human beings and also to identify themselves. Languages have positive and negative influence on life. If the language is delivered with the good it will be a positive influence on those who heard it but, if the language is not delivered correctly it will have a negative effect on those who hear or read it.

In his communication with anyone, we are certainly using the language. According to Dr.Marsigit, there are several levels of communication. Low levels of communication are the communication materials and communication normative. Communication materials used in informal conversation, such as sending SMS to friends, talked with a familiar friend. High levels of communication are the most formal communication and spiritual communication. Communication is used for formal conversation, such as writing formal writing in the blog.

According to Shibutani (1966), features a formal communication channel is a channel that serves as the standard for all reports that come from all sources so that the truth can be checked and a source of the message can be recognized and trusted. So in writing dib log should we use formal communication? Because the blog is a process between individuals (bloggers) who pour each other their work. While the communication related to the spiritual religion. And in my opinion is a spiritual communication between human communications with God through the teachings of each religion. Spiritual communication can be applied in daily life such as running of worship, listen azan, read the holy book and others.

Communication with the spiritual good will the spirituality. According to scholars, the definition of spirituality as a concept that loaded with complex and different meaning, it is used loosely in a different context as religion, architecture, music, esoteric knowledge, etc. So active in communication can improve our knowledge in various fields of life, however, there is also the communication of communication. According Dr.Marsigit disease has two types of communication that is active vocal and union vocal. But the disease that communication can be overcome with a language that we use both every time.

TEST 9_MATHEMATIC NR 07

Nama : Erlina Kurniasih Widyaningrum
NIM : 07305144040
Prodi : Matematika NR 2007
Mata Kuliah : Bahasa Inggris II
Hari, tgl, ruang : Selasa, 18 November 2008, 204
No HP : 081567741616
Email : erlina_dear@yahoo.co.id

VIDEO I
PRE CALCULUS: Graphs of a rational function
• Can have discontinuities has a polynomial in denominator.
• For example:
We have a function f(x) = (x + 2) / (x – 1)
v If value x = 1, we must substitute x = 1 at a function f (x) = (x + 2) / (x – 1) f (1) = (1 +2) / (1 – 1), because one plus two equal three {(1 + 2 = 3)} and one minus one equal zero {(1 – 1) = 0)}, so that the value of three over zero equal infinity {(3 / 0 = ~)}. After value x =1 substitute at rational function will give 0 (zero) in denominator. Further, value x = 1 used bad.
v If value x = 0, we must substitute x = 0 at a function f(x) = (x + 2) / (x – 1)
F (0) = (0 +2) / (0 – 1), because zero plus two equal two {(0 + 2 = 2)} and zero minus one equal negative one {(0 – 1 = 1)}, so that the value of two over negative one equal negative two {(2 / -1= -2)}.
• Not all rational function will give 0 in denominator and can be 0 in denominator.
• Break 2 ways:

v Missing point is a loophole
For example: we have a function y =(x2 – x – 6) / (x – 3).
If value x = 3, we must substitute x = 3 at a function
y = (x2 – x – 6) / (x – 3). We get y = (32 – 3 – 6) / (3 -3). Because three squared minus three minus six equal zero {(32 – 3 – 6 = 0)} and three minus three equal zero {(3 – 3 = 0)}, so that zero over zero not allowed.
We have to factor of x2 – x – 6 become (x – 3) (x + 2). At numerator and denominator there are (x – 3), so that it’s a factor top and bottom. Further, we get value (x – 2) at a function y = (x2 – x – 6) / (x – 3).
v X → 0 in the denominator
v Removable singularity
When x leads 0 / 0, we can do with:
Ø factoring at function
Ø multiplying with the conjugate number

VIDEO II
LIMIT BY INSPECTION
1. x goes to positive / negative infinity
2. Limit involve a polynomial divide by a polynomial
For example:
1. Lim (x3 + 4) / (x2 + x +1)
x→~
Solution:
Easy solution is numerator divide denominator with highest to the power of variable. We look the power of x in numerator and denominator.
At a function highest power of x in numerator is three (3) and highest power of x in denominator is two (2). Because to the power of numerator greater from to the power of denominator, so that the value of Lim (x3 + 4) / (x2 + x +1) = ~
x→~

2. Lim (x2 + 4) / (x3 + 1)
x→~
Solution:
Easy solution is numerator divide denominator with highest to the power of variable. We look the power of x in numerator and denominator.
At a function highest power of x in numerator is three (2).
At a function highest power of x in denominator is two (3).
Because to the power of numerator smaller from the power of denominator, so that the value of Lim (x2 + 4) / (x3 + 1) = 0
x→~
3. Lim (4x3 + x2 + 1) / (3x3 +4)
x→~
Solution:
Easy solution is numerator divide denominator with highest to the power of variable. We look the power of x in numerator and denominator.
At a function highest power of x in numerator is three (3).
At a function highest power of x in denominator is two (3).
Because to the power of numerator equal from the power of denominator, so that the value of Lim (4x3 + x2 + 1) / (3x3 +4) = 4/3
x→~

VIDEO III
EXERCISE
1. If the function h is defined by h(x) = g (2x) + 2. What is the value of h (1)?
Answer:
We will look for value h (1) with h (x) = g (2x) + 2
Because h (1), so that x = 1. We can substitute x = 1 at h (x) = g (2x) + 2
Further, we get h (1) = g (2) + 2
To look for value g (2), we make graph y = g (x). At a graph value from g (2) is 1, so that value from h (1) is three because one plus two equal three.

2. Let the function f be defined by f (x) = x +1. If 2 f (p) = 20
What is the value of f (3p)?
Answer:
What is the f when x = 3p?
2 f (p) = 20, so that twenty divided two equal ten. Further, f (p) = 10
We have a function f (x) = x + 1
For example x = p
We substitute x = p at a function f (x) = x +1, so that it’s become f (p) = p + 1. Because the value of f (p) = 10, so that 10 = p + 1. And the value of p is nine (9). After we get p = 9, we have to substitute p = 9 at x = 3p. The value of x after three times nine is twenty seven.
Because x = 27 and the function f (x) = x + 1 so that, we must substitute x = 27 at a function f (x) = x +1. And the value of f (27) is 28.

3. In the x-y coordinate plane, the graph of x = y2 – 4 intersects line l at (0, p) and (5, t). What is the greater possible value of the slope of l?
Answer:
The graph of x = y2 – 4 intersects line l at (0, p) and (5, t).
For example (0, p) = (x1, y1) and (5, t) = (x2, y2).
The formula of a slope is m = (y2 – y1) / (x2 – x1)
Substitute x1 = 0, x2 = 5, y1 = p and y2 = t at the formula of a slope.
m = (t – p) / (5 – 0)
So that, the greater possible value of the slope of l is m = (t –p) / 5

VIDEO IV
INVERSE FUNCTION
F(x, y) = 0
There are a function y = f(x) (VLT) and x = g(y) (HLT)
For example y = 2x-1 and y = x
§ We get meeting between y = 2x – 1 and y = x
Substitute y =x at y =2x – 1 so that, we get x = 2x-1. After in formulate, we get the value of x is one (1). Because y = x, the value of y also 1 so that, meeting y = 2x-1 with y = x is (1, 1).
§ We get a function y = f(x) and x = g(y)
We have a function y =2x – 1. Because y = f(x) so that, we get the value of f(x) = 2x – 1. We looking for the value of x = g(y), this is the same looking for the inverse of f (x). After y = 2x – 1 formulated, we get x = 1/2 y +1/2. Further, we change the value of y become x and x become y. so that, we get the function of g(x) =1/2x + 1/2.
§ We looking for the composition of a function f g(x) and g f(x)
Firstly, we looking for the composition of a function from f g(x) with substitute g(x) = 1/2x + 1/2 at a 2x – 1 so that, we get f g(x) = 2 (1/2x -1/2) + 1 and if simplified become f g(x) = x.
Second, we looking for the composition of a function from g f(x) with substitute f(x) = 2x – 1 at a 1/2x +1/2 so that, we get g f(x) = 1/2 (2x – 1) + 1/2 and if simplified become g f(x) = x.
Because g = f-1 so that, f g(x) = f (f-1 (x)) = x and also g(x) = f-1 (f(x)) = x given by a function y = (x – 1)/ (x +2). What is the inverse of y(y-1)?
Solution:
Firstly, to looking for the inverse of y = (x – 1) / (x + 2), we must multiplied y and (x + 2) so that, we get y(x + 2) = (x – 1). After that, we formulate the function and we get a function x = (-1 – 2y) / (y – 1). Further, we change the variable of y become x and also x become y. so that, we get the function of y-1 = (-1 – 2x)/(x-1). If y-1 = 0 so that, the function become (-1 – 2x) / (x – 1) = 0. Further, multiplied (x – 1) with 0 so that, we get x = - 1/2.