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Often, you might experience that applying limits results in infinity. In limits, getting infinity means something isn't right. Mathematicians dislike infinity results, but why? What is infinity and what it means in the world of limits?
What is Infinity?
Before we explain what is infinity, we want you to solve a division question, divide 
by 
(i.e. 
). What quotient did you get? Is it 
or 
? The problem is, we don't know! If we start writing 
from the first page of a notebook and fill the whole notebook with still it is nothing! It will go on forever because you can't divide any number by zero. In simple words, it is undefined! And the best way to show that it will go forever, we use the infinity sign, 
. In the mathematics world, infinity means that a value that isn't defined. It is endless and we can't define that value. The best part is that we can't find this value but still we can work with it.
Infinity in Limits
Infinity can be found in every domain of maths. However, if we talk about the domain of maths that most likely will end up with infinity then limits might win. Limit means that we are testing the limit of the equation. This doesn't mean that every time we apply limits to any equation will always end in infinity. It mostly depends on the equation, for example, you have an equation, 
and you applied limits at 
, what would you get? Of course, it will be infinity! But here we are testing the limits of the equation, we found that at , the equation results in infinity.
In this example, only at , the function outputs infinity but all the values other than 
and , you will get a real number. At a certain point where the function reaches infinity, our keen point would be the point before the function outputs infinity. It could be 
but there is a problem, it can still go to infinity! How many 
will you add? That is why we use different methods to find the limits at infinity.
Below are more examples how you can end up with infinity in limits.
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Correct equals infinity equals 16 but not true. It’s it’s six it’s infinity.
∞ = -1/12
By Sriniwas aramanujan
And this, my friends, is why humans will be conquered by AI… so many logic holes it’s… well, infinite. lol
Is 0^infinity ( zero to the power infinity) indeterminate form? How?
Didn’t Cantor proved that there are a group of infinities (the Aleph zero & Aleph one sets, for example)? And these are grouped around the concept of infinite to the power infinity, if I remember correctly .
Exercise 3
I think it is discontinuous at 0
exercise 2 : the function is not defined for x= 0.
exercise 1 q 5 The function has a jump discontinuity at x = 1, should be x=0.