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I'M thinkng of a fuction
hat continus increasin without limit
the ES itS domain

IT has a Rang lacking diSjunctioN
which cannot acint with
is dismal lowr lane

Through ELiinG and xpunction
you may arive ye at it
f you don't orthink.

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  • $\begingroup$ @ArkaKarmakar just post your own answer then, instead of commenting on everyone else's? I'm curious how that's trivial, because I thought of that phrase also but didn't see how to make it work. $\endgroup$ – user812786 Sep 13 '16 at 15:58
  • $\begingroup$ @whrrgarbl: When you see integral e__ derivative, and it's not an Math stackexchange site, there is a huge probably it is something to do with equal, so I guessed it and took the chance. And I have a bad rep in answering, so it might get downvoted if it is a red herring. $\endgroup$ – user27395 Sep 13 '16 at 16:01
  • $\begingroup$ @Strawberry: Who ? $\endgroup$ – user27395 Sep 13 '16 at 16:03
  • $\begingroup$ @ArkaKarmakar where do you see "derivative"? I agree the first two are easy to find, but that's where I got stuck. $\endgroup$ – user812786 Sep 13 '16 at 16:04
  • $\begingroup$ @whrrgarbl: Random educated guessing. I was guessing, and I am bad at it, so I posted a comment. $\endgroup$ – user27395 Sep 13 '16 at 16:05
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A possible answer:

$f(n)$ $=$ $e$$n$

the Exponential Function

Others have pointed out that 'A Dearth at Sea' means to leave out any constant

The Capitals spell out

IMESSITRSNTELG

Which @JonathanAllan has found is an anagram of

MISSING LETTERS

So we need to focus on the missing letters

There are also some letters that are missing from the riddle though it is hard to make out the intended words...

I think the riddle is trying to say:

I'M thinking of a function
that continues increasing without limit
the rEalS itS domain (Thanks @DanRussell)

IT has a Range lacking diSjunctioN
which cannot acquaint with
its dismal lower lanes

Through ELidinG and expunction
you may arrive yet at it
if you don't overthink.

So so far the missing letters are:

integral equates der?ive (derivative?)

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  • 1
    $\begingroup$ Letters missing. $\endgroup$ – Jonathan Allan Sep 13 '16 at 15:20
  • $\begingroup$ @ArkaKarmakar, it will be difficult to fit "iva" between the "r" and "t" of "arrive" and "yet"... $\endgroup$ – Ian MacDonald Sep 13 '16 at 15:57
  • $\begingroup$ @IanMacDonald: See Dan Russel's answer. $\endgroup$ – user27395 Sep 13 '16 at 15:59
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    $\begingroup$ @ArkaKarmakar, Dan Russel's answer posits "derivative" using the letters "dertive". It is missing the "iva", as I suggested. $\endgroup$ – Ian MacDonald Sep 13 '16 at 16:47
  • $\begingroup$ @IanMacDonald: Oh, yeah, you are right. I didn't read it mindfully. $\endgroup$ – user27395 Sep 13 '16 at 16:48
8
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Most likely

The function you are thinking of is $f(x) = e^{x}$, the exponential function.
The title clue is "A dearth of sea", so no $+c$, no constant added.

The

capitals are an anagram of MISSING LETTERS

So we should look at them...

I think they are: INTEGRAL EQUATE DERIVE:

i'm thinkIng of a fuNction
That continuEs increasinG without limit
the ReALs ARE its domain

it has a rangE lacking disjunction
which cannot acQUAint with
iTs dismal lowEr lane

through eliDing and Expunction
you may arRive ye at it
If you don't oVErthink.

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  • $\begingroup$ Oh wait, there is no "S" for that first word... $\endgroup$ – Jonathan Allan Sep 13 '16 at 15:52
  • 1
    $\begingroup$ And the T at the start of th last para is already there too $\endgroup$ – Beastly Gerbil Sep 13 '16 at 15:53
7
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The final answer is probably

$y=e^x$, because its integral equals its derivative.

(N.B. that the title's "death of sea" means to leave out any constant $C$ to ensure this is true.)

As pointed out by others, the capital letters

are an anagram of "MISSING LETTERS".

I think all the missing letters from the first paragraph spell

integral

I'M think(i)ng of a fu(n)ction
(t)hat continu(e)s increasin(g) without limit
the (r)E(al)S itS domain

The second paragraph

equates

IT has a Rang(e) lacking diSjunctioN
which cannot ac(qua)int with
i(t)s dismal low(e)r lane(s)

A possiblity for the third paragraph is

derivative?

Through ELi(d)inG and (e)xpunction
you may ar(r)ive ye(t) at it
(i)f you don't o(ve)rthink.

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  • $\begingroup$ OK almost the same as my answer :) $\endgroup$ – Jonathan Allan Sep 13 '16 at 16:18
  • $\begingroup$ @JonathanAllan Ah, yes. All working on it in parallel apparently! $\endgroup$ – Dan Russell Sep 13 '16 at 16:18
  • $\begingroup$ I'm sticking with the olde English "You may arrive ye at it" :) $\endgroup$ – Jonathan Allan Sep 13 '16 at 16:19
  • $\begingroup$ @JonathanAllan Which I like, but I remember my calculus teacher from high school: "differentiate, not derive!" $\endgroup$ – Dan Russell Sep 13 '16 at 16:20
5
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Another try:

Missing letters (anagram credit to Jonathan Allen!) in parentheses:

I'M think(i)ng of a fu(n)ction
(t)hat continu(e)s increasin(g) without limit
the (r)E(al)S itS domain

IT has a Rang(e) lacking diSjunctioN
which cannot ac(qua)int with
i(t)s dismal low(e)r lane

Through ELi(d)inG and (e)xpunction
you may a(r)rive ye at it (yet?)
(i)f you don't o(ve)rthink.

This gives the words:

integral, equate, derive

Title refers to:

The constant of integration (typically + C)

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