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Not everything is defined in maths. In fact, there are some regions in maths which we can't even imagine. Anything that can't be defined by maths is called an indeterminate form. An indeterminate form does not mean that the limit is non-existent or cannot be determined, but rather that the properties of its limits are not valid. In these cases, a particular operation can be performed to solve each of the indeterminate forms. In simple words, you need to have a different approach to handle such problems, many mathematicians use the differentiation method to solve the indeterminate form but this is not the only method, there are several methods which you can use but let's just stick to the indeterminate forms with its types for now.
Indeterminate Form
Indeterminate form comes in various shapes. To understand the indeterminate form, it is important to learn about its types.
1. Infinity over Infinity
For example, you are given a function, 
. After applying limits, you will get 
which can't be solved. There is no proper solution of this fraction and that is why we can conclude it as an indeterminate form.
2. Infinity Minus Infinity
When you subtract infinity from infinity. Again there is ambiguity in the equation. You cannot minus infinity from infinity, we can't find a proper outcome. Hence, it is considered an indeterminate form.
3. Zero over Zero
One of the most common indeterminate examples is zero over zero. Dividing any number by zero is undefined, it could be any value. The reason is that the division will never be completed. You keep dividing the numerator with zero and it will keep going till infinity. Therefore, zero over zero is a very common indeterminate form.
4. Zero Times Infinity
We talked about infinity over infinity, and zero over zero, what about zero times infinity? The answer is undefined again! It could be any number that we can't predict. Many people make this mistake, they think that the answer is zero because anything multiplied by zero is zero but what they don't realize is the infinity sign with it.
5. Zero to the Power of Zero
This problem is similar to the division by zero. Mathematics rule says that any positive number, besides zero, whose power is equal to zero will be equal to one. So, it means 
is 
but how can a zero entity be equal to one? It is impossible for zero to become one or any other number at any cost. Hence, it is undefined and we can call it an indeterminate form.
6. Infinity to the Power of Zero
Infinity value doesn't have a universal value. Infinity having a power equal to zero is also undefined hence it is also a type of indeterminate form.
7. One to the Power of Infinity
Last but not least, one to the power infinity is also a type of indeterminate form. Since we don't know the value of infinity, we couldn't define 
.
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Derivative of denominator is wrong
Good catch—thanks for pointing that out! We’ll double-check the derivative in that section and make any necessary corrections. Really appreciate you taking the time to flag it. 👍
Thank you
Thank you Abbas! Good luck with your studies!
With regard to the Zero Over a Number item, is there a mis-statement? It’s immediately followed by “If a number is divided by zero which means that the numerator is zero and the denominator is the number, then the result is zero.”
Hi Mark,
You’re absolutely right to raise the question — there does appear to be a misstatement in that sentence. The phrase “If a number is divided by zero, which means that the numerator is zero and the denominator is the number…” is indeed misleading and should be corrected.
To clarify:
Zero divided by a number (e.g. 0 ÷ 5) equals 0.
A number divided by zero (e.g. 5 ÷ 0) is undefined.
We’ll update the sentence to reflect the correct mathematical explanation. We appreciate you catching that and helping us improve the accuracy of the content!
There is more than one size of infinity, though. What if you multiply the infinity of the whole numbers (Aleph-0) by the infinity of the real numbers (fraktur-c)?
Thanks a lot to you for this essentiol article.
Hi Piyash! Thanks for your comment, great to hear that you found this useful!
Very nice