Question

Explain why a limit does not exist when 𝑥 approaches to 2 for 𝑓(𝑥) = √2 − 𝑥

Answer 1

assuming you mean √(2-x),
because f(x) is undefined for x > 2

Answer 2

I would say the limit does not exist when x approaches to 2 for that equation is because thing of the x approaching 2.
It can either come from left or right (Positive side or Negative side)
so plugging that in the equation it will look something like this.

**Understand that the negative sign is not an actual sign but just letting you know its from the left side approaching 2


Positive side: f(+2)=√2-(2+) = √-0
Negative side: f(-2)=√2-(2-) = √+0

Now √-0 and √+0 are very different. The √-0 is not possible because of the -(sign) you are not able to square root a negative number, while √+0 is possible so it would = 0.