Can someone explain this calculus shit to me? I missed last

Pleading bump

Please someone explain this to me, I'll give you 5 (you)s.

Man I don't wanna brag but I barely remember this shit. It's literally not even important. Just skip it.

>>9165080
I would 100% skip this if my grade didn't depend on knowing it, at least the upcoming test and homework grade. Trust me, I throw half the stuff I learn straight out the window after the class ends, but that's not the point here.

What is your question? You say you know what delta and epsilon represent but don't understand

>>9165090
How tf is a 2 and b is .5

>>9165080
Find the brainlet

>>9165081
What is the definition of limit? If you think about it for some time, try to draw the epsilon in the graph, and see what delta has to be from the definition of limit.

Maybe look at some visual explanaiton of limit as well

a.)
f(x) - 6 < 3
and f(x) - 6 > -3.
Rearranging/combining the above two lines,
we get 3 < f(x) < 9.
This condition holds when 1 < x < 5 by looking at the graph.

Or when -2 < (x - 3) < 2.
Which is equivalent to saying |x-3| < 2.

It's the same thing for part b.
Just start off with:
f(x) - 6 < 1
and
f(x) - 6 > -1.
Then f(x) < 7 and f(x) > 5.
This happens on the graph when 2.5 < x < 3.5.
Or when -0.5 < x < 0.5
Or equivalently |x| < 0.5.

Me again. This isn't even calculus.
This is just reading a graph.

>>9165100
This is calculus, this is probably the essence of calculus that most eng brainlets won't even see - and also the reason some weird shit can be made int calculus, dealing with stuff going to infinity and similar stuff.

God fucking damnit I messed up the last 2 lines of my answer.
Change the last 2 lines to
Or when -0.5 < x-3< 0.5
Or equivalently |x-3| < 0.5.

>>9165099
Not op but thanks

>>9165099
>>9165108
This is actually starting to make a lot more sense. I was trying to solve it mathematically or something instead of just looking at the graph. I got to the 3 < f(x) < 9 part but didn't know what to do with that. Thanks!

>>9165116
No problem.
And when I say this isn't a calculus problem, I just mean it doesn't involve any differentiation or integration.

>>9165100
What? This is a calc 1 concept. Though you are sorta right in the sense that finding the answer to the problem does rely a little bit on staring at a graph of the function. However, as >>9165099 's post clearly demonstrates, this problem goes a little deeper than that and does use some notation.