Chapters
The concept of infinity comes from division by zero. Imagine you have 15 pencils, you need to divide them into zero people, how much did each person get? It would be nothing! Because nothing is given to them. In mathematics, when you divide any number by zero, it will result in infinity. For example, divide 
by 
, the division will go on forever but you will achieve nothing. The answer will be undefined. Finding the limit of an expression that is divided by zero can be either 
or no limit.
For example, you are asked to find the limit of 
which is approaching 
. Let's replace 
with and find what would we get:
One thing is clear, you will get infinity but what is the sign? Is it either positive infinity or negative infinity? To find that, we will be performing the side limits to determine the sign of 
.
If x has a value that approaches from the left, 
, both the numerator and denominator are negative and the left side limit is: 
.
If x has a value that approaches from the right, 
, the numerator will be negative, the denominator positive and therefore the right-side limit will be: 
.
The next step is to find whether the function has an output on that input. To best way to find that is to check the side limits, if they coincide, that means the function has an output for that input. Since the side limits do not coincide, the function has no limit as 
Example
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Correct equals infinity equals 16 but not true. It’s it’s six it’s infinity.
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.