R.E.S.T-10

Sunday, August 8, 2010 | By Ariff

Pada 5hb-7hb ogos yang lalu..PP UMnp telah menganjurkan sebuah aktiviti rehlah saqafah (rest). Ia terbuka kepada pelajar semester 1..tidak ketinggalan siswa-siswi APIDS.

Program ini bertujuan untuk mengeratkan ukhwah antara PP dan siswa-siswi sem 1. Selain itu, program ini adalah untuk merehatkan siswa-siswi dari pelbagai bentuk masalah di UM seperti assignment, rifqah dan program2 lain.

Antara slot2 yang terdapat dalam program ini adalah seperti slot kepentingan tarbiyah dlm kalangan mahasiswa yang disampaikan oleh Prof. Madya Dr Shukeri, slot Mesra bahasa Arab yang disampaikan oleh Ustaz Norhazrul dan slot bersama Akh Shahrul Nizam dan banyak lagi. Disamping itu, program ini turut mengadakan aktiviti melakukan assginment bersama2 Fasi, aktiviti BBQ di PCB, slot debat Dakwah Vs Study dan lain.

Semoga semua siswa-siswi APIDS mendapat manfaat daripada program ini dan mengaplikasikannya dalam kehidupan seharian. Ambil yang jerneh buang yang keruh. Sama2lah memperbaiki diri untuk masa yang akan mendatang. Kami bagi pihak APIDS mengharapkan lebih banyak aktiviti seperti ini dianjurkan yang melibatkan kami.
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Snoring , not Funny not hopeless

Tuesday, August 3, 2010 | By Ariff

Some 45% of normal adults snore at least occasionally, and 25% are habitual snorers. Problem snoring is more frequent in males and overweight persons, and it usually grows worse with age.

More than 300 devices are registered in the U.S Patent and Trademark Office as cures for snoring. Some are variations on the old idea of sewing a tennis ball on the pajama back-to force the snorer to sleep on his side. (Snoring is often worse when the person sleeps on his back). Chin and head usually disappointing as snoring cures. Many electrical devices have been designed to produce painful or unpleasant stimuli when the patient snores. The presumption was that a person could be trained or conditioned not to snore. Unfortunately, snoring is not under the person’s control whatsoever; and if these work. It is probably because they keep the snorer awake.

What cause snoring?? The noisy sounds of snoring occur when there is an obstruction to the free flow of air through the passages at the back of the mouth and nose. This is collapsible part of the airway where the tongue and upper throat meet the soft palate and uvula (the fleshy structure that dangles from the roof of the mouth back into the throat). When these structures strike against each other and vibrate during breathing- that is snoring. Persons who snore have at least one of the following problems:

1. Poor muscle tone (lack of tightness) in the muscle of the tongue and throat.

2. Excessive bulkiness of tissues of the throat.

3. Excessive length of the soft palate and uvula.

4. Obstructed nasal airway.

Also, deformities of the nose or nasal septum frequently cause such obstruction. “deviated septum” is a common term for a deformity inside the nose in the wall that separates one nostril from the other.

Can snoring be cured? By far the majority of snores can helped. For adults who are mild or occasional snores, the following self-help remedies are worth trying.

1. Adopt an athletic life-style and exercise daily to develop good muscle tone and loose weight.

2. Avoid tranquilizers, sleeping pills and antihistamines before bedtime.

3. Avoid alcoholic beverages within 4 hours of retiring.

4. Avoid getting overtired; establish regular sleeping patterns.

5. Sleep sideways rather than on the back. Consider sewing a pocket on the pajama back to hold a tennis ball. This help to avoid sleeping on your back.

6. Tilt the entire bed with the head upward 4 inches.

7. Allow the non-snorer to get sleep first.

Remember! Snoring means obstructed breathing, and obstruction can be serious. It is not Funny and it is definitely not Hopeless.

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Dua Hari Bersama Lect PASUM..

Friday, July 30, 2010 | By Ariff

Pada 26hb julai yang lalu, Dr Fadzilah yang merupakan pensyarah bg subjek Algebra & Geometri (FJAX0111) di UM Kuala Lumpur telah hadir ke APIUM Nilam Puri untuk membantu siswa-siswi APIDS yang juga mengambil subjek ini. Kehadiran beliau telah membantu siswa-siswi dalam memahami subjek ini dengan lebih efisyen. Jutaan terima kasih kepada beliau yang sanggup datang dari jauh untuk membantu kami siswa-siswi APIDS disini berkongsi ilmu mungkin dengan cara yang lebih mudah.

Pada 27hb pula, Dr Hj Ismail yang merupakan pensyarah bg subjek Calculus (FJAX0112) di UM Kuala Lumpur juga telah hadir ke sini, APIUM Nilam Puri untuk menambah serba sikit apa yang dirasai perlu ditambah oleh beliau. Jutaan terima kasih juga diucapkan kepada beliau atas kesudiaan untuk berkongsi ilmu dengan kami.

Diharap kepada warga APIDS tidak mensia-siakan ilmu yang dicurahkan oleh mereka malah akan saling membantu antara kita sama sendiri.
p/s=lupa nk tgkap gmbar Dr Hj Ismail..hehe
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PERJUMPAAN BERSAMA SENIOR APIDS

Wednesday, July 14, 2010 | By Ariff
Hmm....ini adalah perjumpaan siswa-siswi APIDS dgn senior APIDS which is now they proceed their study in sem 3 at UM, KL....mreka dtg ke UM nilam puri adlh untuk bercerita serba sedikit tentang pgalaman mreka disini dan bgaimana mereka mlalui ksukaran compete dengan siswa-siswi PASUM....
selain itu mereka juga telah menerangkn serba sedikit mgenai course APIDS dan marketnya....

pada akhir perbincangan mereka menunjukkan slide show mgenai program-program y mreka telah jlnkn dibwah organisasi APIDS seperti X-Disc, Pesta buah, Pesta Layang2, Futsal, Kem n so on....

dengan lebih ringkas disini, boleh ana katakn kedatangan mereka disini adlah lebih btujuan ingin mnjadikan kami siswa-siswi y lebih berefisyen, beretika serta berdaya saing. mereka telah memberi dorongan serta semangat y tggi kepada siswa-siswi untuk terus menaikkn nama APIDS selaku insan y seimbang ilmu duniawi dan ukhrawi....
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Limits and Infinity

| By Ariff

One of the mysteries of Mathematics seems to be the concept of "infinity", usually denoted by the symbol $\infty$. So what is $\infty$? It is simply a symbol that represents large numbers. Indeed, numbers are of three kinds: large, normal size, and small. The normal size numbers are the ones that we have a clear feeling for. For example, what does a trillion mean? That is a very large number. Also numbers involved in macro-physics are very large numbers. Small numbers are usually used in micro-physics. Numbers like 10-75 are very small. Being positive or negative has special meaning depending on the problem at hand. The common mistake is to say that $-\infty$ is smaller than 0. While this may be true according to the natural order on the real line in term of sizes, $-\infty$ is big, very big!

So when do we have to deal with $\infty$ and $-\infty$? Easy: whenever you take the inverse of small numbers, you generate large numbers and vice-versa. Mathematically we can write this as:

\begin{displaymath}\frac{1}{0} = \pm \infty\;\;\mbox{and}\;\; \frac{1}{\infty} = 0\;.\end{displaymath}

Note that the inverse of a small number is a large number. So size-wise there is no problem. But we have to be careful about the positive or negative sign. We have to make sure we know whether a small number is positive or negative. 0+ represents small positive numbers while 0- represents small negative numbers. (Similarly, we will use e.g. 3+ to denote numbers slightly bigger than 3, and 3- to denote numbers slightly smaller than 3.) In other words, being more precise we have
\begin{displaymath}\frac{1}{0+} = +\infty\;\;\mbox{and}\;\; \frac{1}{0-} = -\infty\;.\end{displaymath}

Remark. Do not treat $\pm\infty$ as ordinary numbers. These symbols do not obey the usual rules of arithmetic, for instance, $\infty +1=\infty$, $\infty -1=\infty$, $2 \cdot\infty=\infty$, etc.

Example. Consider the function

\begin{displaymath}f(x) = \frac{1}{x-3}\;\cdot\end{displaymath}

When $x \rightarrow 3$, then $x-3 \rightarrow 0$. So
\begin{displaymath}\lim_{x \rightarrow 3-} f(x) = \frac{1}{0-} = -\infty\;\;\mbo... ...d}\;\; \lim_{x \rightarrow 3+} f(x) = \frac{1}{0+} = +\infty\;.\end{displaymath}

Note that when x gets closer to 3, then the points on the graph get closer to the (dashed) vertical line x=3. Such a line is called a vertical asymptote. For a given function f(x), there are four cases, in which vertical asymptotes can present themselves:

(i)
$\displaystyle \lim_{x \rightarrow a-} f(x) = -\infty$; $\displaystyle \lim_{x \rightarrow a+} f(x) = -\infty$;
(ii)
$\displaystyle \lim_{x \rightarrow a-} f(x) = -\infty$; $\displaystyle \lim_{x \rightarrow a+} f(x) = +\infty$;
(iii)
$\displaystyle \lim_{x \rightarrow a-} f(x) = +\infty$; $\displaystyle \lim_{x \rightarrow a+} f(x) = -\infty$;
(iv)
$\displaystyle \lim_{x \rightarrow a-} f(x) = +\infty$; $\displaystyle \lim_{x \rightarrow a+} f(x) = +\infty$;

Next we investigate the behavior of functions when $x \rightarrow \pm\infty$. We have seen that $\displaystyle \frac{1}{\pm \infty} = 0$. So for example, we have

\begin{displaymath}\lim_{x \rightarrow -\infty} \frac{1}{x} = 0\;\;\mbox{and}\;\; \lim_{x \rightarrow +\infty} \frac{1}{x} = 0\;.\end{displaymath}

In the next example, we show how this result is very useful.

Example. Consider the function

\begin{displaymath}f(x) = \frac{2x+1}{x-1}\;\cdot\end{displaymath}

We have
\begin{displaymath}\frac{2x+1}{x-1} = \frac{2+\displaystyle \frac{1}{x}}{1-\displaystyle \frac{1}{x}}\end{displaymath}

which implies
\begin{displaymath}\lim_{x \rightarrow \pm \infty} f(x)= \frac{2+0}{1-0} = 2\;.\end{displaymath}

Note that when x gets closer to $\pm\infty$ (x gets large), then the points on the graph get closer to the horizontal line y=2. Such a line is called a horizontal asymptote.

In particular, we have

\begin{displaymath}\lim_{x \rightarrow -\infty} \frac{a}{x^r} = 0\;\;\mbox{and}\;\; \lim_{x \rightarrow +\infty} \frac{a}{x^r} = 0\end{displaymath}

for any number a, and any positive number r, provided xr is defined. We also have
\begin{displaymath}\lim_{x \rightarrow \infty} x^r = \infty\;.\end{displaymath}

For $-\infty$, we have to be careful about the definition of the power of negative numbers. In particular, we have
\begin{displaymath}\lim_{x \rightarrow -\infty} x^n = (-1)^n \infty \end{displaymath}

for any natural number n.

Example. Consider the function

\begin{displaymath}f(x) = \frac{2x^4 -3x^2 + 5}{3x^4 + 2x +5}\;\cdot\end{displaymath}

We have
\begin{displaymath}\frac{2x^4 -3x^2 + 5}{3x^4 + 2x +5} = \frac{\displaystyle 2 -... ...5}{x^4}}{\displaystyle 3 + \frac{2}{x^3} +\frac{5}{x^4}}\;\cdot\end{displaymath}

So we have
\begin{displaymath}\lim_{x \rightarrow \pm \infty} f(x) = \frac{2 -0 + 0}{3 + 0 +0} = \frac{2}{3}\;\cdot\end{displaymath}

Example. Consider the function

\begin{displaymath}f(x) = \frac{\sqrt{4x^2 +2}}{3x+1}\;\cdot\end{displaymath}

We have
\begin{displaymath}\sqrt{4x^2 + 2} = \sqrt{x^2\left(4 + \frac{2}{x^2}\right)} = \vert x\vert \sqrt{4 + \frac{2}{x^2}}\end{displaymath}

and then
\begin{displaymath}\frac{\sqrt{4x^2 +2}}{3x+1} = \frac{\vert x\vert}{x} \frac{\d... ...ystyle \sqrt{4 + \frac{2}{x^2}}}{\displaystyle 3 + \frac{1}{x}}\end{displaymath}

When x goes to $+\infty$, then x > 0, which implies that |x| = x. Hence
\begin{displaymath}\lim_{x \rightarrow +\infty} f(x) = \frac{\sqrt{4 + 0}}{3 + 0} = \frac{2}{3}\;\cdot\end{displaymath}

When x goes to $-\infty$, then x <>x| = -x. Hence
\begin{displaymath}\lim_{x \rightarrow -\infty} f(x) = -\frac{\sqrt{4 + 0}}{3 + 0} = -\frac{2}{3}\;\cdot\end{displaymath}

Remark. Be careful! A common mistake is to assume that $\sqrt{x^2} = x$. This is true if $x \geq 0$ and false if x <>

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