_{1}

In this paper, I’m going to discuss on why are
^{0},
, and
indeterminate form using simple calculus and algebra.

There are so many things that they are undetermined/indeterminate. Our universe is too complex to model mathe- matically because most of them are undetermined/indeterminate, but we have mathematical model for indeter- minate things itself called indeterminate forms. For example, the weight and height of human beings is indeter- minate because we can’t say the weight or height of human being is this much.

Everything we don’t know is infinitely many times more than everything we know. From something we know we can creat something we don’t know and that gonna be something we know and using this something we know we can creat another something we don’t know and it will continue and never ending. For example, let the only thing we know is hydrogen and oxgen but if we combine two hydrogen and one oxgen we can creat another thing, say water and by combining alot of water together we can creat another thing, say river, lake, ocean etc and also if we add something in to the river or lake or ocean we may creat another living things that we haven’t seen them before and we can continue in such away that creating something we don’t know from something we know.

Someone may ask the main question, “What is the thing before something ?”. In other words, where is our universe comes from? Is our universe comes from something or from nothing? If we assume that our universe is created by God and then some one may ask, “Where God comes from and where he was before he creat the universe?” and Some one may answer for this question like “Before God there is nothing and God comes from nothing”. This may indicates that there is something from nothing [

something by c, then

which means doesn’t exist. Here we can’t say anything about nothing while nothing exists but invisible. Till

now the first and the only thing we imagine about c is, c might be God or Big-bang. To be something exist there should be nothing exist first. Empty-space doesn’t imply that nothing and vice versa since nothing is not mea- surable and not observable but existance [

In calculus and other branches of mathematical analysis, limits involving algebraic combination of functions in an independent variable may often be evaluated by replacing these functions by their limits; if the expression obtained after this substitution does not give enough information to determine the original limit, it is said to take on an indeterminate form. The term was originally introduced by cauchy’s student Moigno in the middle of the 19th century.

The indeterminate forms typically considered in the literature are denoted

Definition: The function

Theorem 1. The number

Proof. We know that the laplace transform of 1 is equal to

But if

Therefore

Corollary 1.

Proof.

Theorem 2. The number

Proof. We know that the laplace transform of 1 is equal to

Let’s replace s by

But if

Therefore

Corollary 2.

Proof.

Theorem 3.

Proof. Easily sketched from Theorem 1-2 and Corollary 1-2.

Theorem 4. The function

Proof. From above Theorem-1 we have,

If we take natural logarithm both sides of this equation we get,

Remark: For every natural numbers m and n such that

1.

2.

3.

4.

Theorem 5. The number

Proof. Let’s take any arbitrary constants

We know that

this implies that for every natural numbers m and n

From this we must therfore conclude that

Theorem 6. If

Proof. Suppose

Therefore

This theorem shows that

Theorem 7. The number

Proof. Suppose

Therefore

Let’s suppose that

Thus

Theorem 8. The number

Proof. Let’s take any arbitrary constants

We know that

this implies that for every natural numbers m and n,

From this we must therefore conclude that

Theorem 9. The number

Proof. Since

Theorem 10. The number

Proof. Suppose

but from our assumption

Therefore

Let’s suppose that

Thus

Theorem 11. The number

Proof. Let’s take any arbitrary constants

We know that

this implies that for every natural numbers m and n such that

From this we must therefore conclude that

Theorem 12. The number

Proof. Suppose

but from our assumption

Therefore

Let’s suppose that

Thus

Theorem 13. The number

Proof. Let’s take any arbitrary constants

We know that

Thus for every natural numbers m and n such that

From this we must therefore conclude that

Theorem 14. The number

Proof. Suppose

Therefore

Let’s suppose that

Thus

Theorem 15. The number

Proof. We know that

But if

Theorem 16. The number

Proof. We know that

But if

Corollary 3.

Proof. We know that

But if

Theorem 17. The number

Proof. We know that

But if

for

Corollary 4.

Proof. We know that

But if

Dagnachew Jenber, (2016) Indeterminate Forms. Advances in Pure Mathematics,06,546-554. doi: 10.4236/apm.2016.68043