l'maancha Elokim chaim

In parshas Ki Teitzei, Rashi (22:8) explains the smichus ha'parshiyos, the juxtaposition of the mitzvah of shiluach ha'kan with the mitzvah to build a maakah and then the mitzvah of not plowing with kilayim of a donkey and ox and the mitzvah of not wearing kilayim: 

כי תבנה בית חדש ועשית מעקה וגו׳ – אם קיימת שילוח הקן, סופך לבנות בית, ולקיים מצות מעקה, שמצוה גוררת מצוה, ותגיע לכרם ושדה ובגדים נאים. לכך נסמכו פרשיות הללו.

If you fulfill shiluach ha'kan, writes Rashi, you will be zocheh to build a house and do the mitzvah of maakeh, and then you will be zocheh to have a field and vineyard that need plowing and will keep the issue of kilayim, and you will have beautiful clothes to wear and you will get to fulfill the mitzvah of shaatnez.  

Shem m'Shmuel asks: Schar mitzvah b'hai alma leika!?  The reward for mitzvos comes only in the next world, not in this world.  Why here do you get a new house, a field, a vineyard, nice clothes one right after the other in this world for doing these mitzvos? 

Schar mitzvah b'hai alma leika, he explains, because reward is the tachlis, the end result.  The world of tachlis is the next world; this world is just the world of hachana, where everything is a means to the end, but not an end in itself.  If you are collecting schar a final reward for the hard work you put in, then you have to wait until you get to the next world.  But if the schar you are collecting is itself a means to a greater end, then that falls under this world, the world of means.  When you get a house not to show everyone the new kitchen you put in but rather as a means to do other mitzvos like maakah; when you have a field or vineyard not just to build your wealth but as a means to fulfill kilayim; when the clothes you wear are not to show off your new outfit but because you are mekayeim shaatnez and other mitzvos, then Hashem piles on more so that you can do more.  (Compare with Rambam in Hil Teshuvah perek 9).

Now we understand what we mean when we say, "Zachreinu l'chaim..,. l'maancha Elokim chaim."  We ask Hashem for life, we ask Hashem for so many other things.  Schar b'hai alma leika, why should we imagine we will get any of it?  The answer is, "L'maancha Elokim chaim."  We're not asking just to satisfy our own selfish needs, but we're asking so that we can use what we get "lmaancha," for your sake Hashem.  It's all just a means so that we can be better ovdei Hashem.

If that's the attitude you bring to your bakashos in davening, then hopefully you won't be turned away.

Kiddushin 25a:

 הכל מודים בלשון לענין טומאה דגלוי הוא

The gemara writes that the tongue, the mouth, is considered "galuy," a revealed, open place.  If a sheretz comes in contact with a person's tongue, the person is tamei; it's not maga beis ha'starim.  

A person can articulate and express through the tongue and the mouth things that are "galuy," that he/she can to reveal and communicate to others.

But there is a whole deeper level of pnimiyus in a person that is not galuy, that the mouth and tongue cannot formulate into words, that we can't articulate either to others or maybe not even to ourselves.  That's the kol shofar.  That's the cry that  cannot be formulated into words, but which stirs inside of us.

That's the kol that we cry to Hashem with on Rosh haShana.