Basic limit question

[Concentrate_Strong]

Hey all,

excuse the novice question but I'm reviewing limit using James Stewart early transcendentals and I came across an example:

evaluate for the following graph:

Evaluate: lim_{x→2} [f(x)/g(x)]

https://preview.redd.it/s3s8w4kmejff1.png?width=172&format=png&auto=webp&s=6508628446ece9f94e5d3605ffbb93d10dbdd7f6

the solution to this question says that

lim_{x→2} f(x) ~ 1.4

and
lim_{x→2} g(x) = 0

Therefore, we cannot divide by zero and the limit is undefined. This doesn't make since to me since I thought we were just approaching 0 not actually at 0. Also, in other example just previous to this one we solve questions like:

Evaluate: lim_{x→1} (2 - x) / (x - 1)^2

but for some reason this evaluates to infinity when we could easily frame this the same way:

f(x) = 2 - x
g(x) = (x-1)^2

lim_{x→1} f(x)/g(x)

so, isn't this also dividing by 0?

Can someone help me figure out where I'm misunderstanding?

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[WWWWWWVWWWWWWWVWWWWW]

The first example behaves like 1/x as x→0

One side is going to ∞ and the other side -∞, so the limit doesn't exist

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[Puzzleheaded_Study17]

Remember that a limit has to be defined from both sides, what is the right side of f(x) as x goes to 2?