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sure

they are usually not nearly as hard as they look

do we really have to sketch them?

or can we just find the limits if they exist?
that is much easier than drawing

ok lets start with the first one

Thank you!

the definition of the function changes at 2 right?

Yes

guess what we do next?

we are not done yet, we just checked the limit as x goes to 2

and yah just plug it in

we also need to check if it goes to 4?

right

plug in 4 as well?

yeah plug in 4 to the middle one and the bottom one and see if you get the same answer (you do not)

Okay, thank you for explaining.

Since I have to plug 4 into the functions

you are quite welcome
told you it was easy right? math teachers often make it seem harder than it is

yeah but only in the middle one and the bottom one where it changes from
\[8-2x\] to \[4\]

Since i have to plug 4 into the functions, does that mean that 4 is not part of the limit?

i am not sure what you are asking

if you plug 4 in to \[8-2x\] you get 0 right?

that the limit for the function exists everywhere else but 4. is that the correct?

yes, that's what i got when i plugged it in.

ok and to the right,the function is a constant, it is just 4

so that means, since \(0\neq 4\) you have
\[\lim_{x\to 4}f(x)\] does not exist

give me a second and i will show you a graph

taking me a second, but soon

so my final answer would be
lim f(x)
x->2
and lim f(x)
x-4 does not exist

you're fine, take your time. i really appreciate the help.

yes
picture almost done
damn syntax is killing me

oh just click on it

and yes, that is your final answer for the limits from the first question
graph is what i linked to

okay, thank you so much! that was incredibly helpful!
I'll try the next one on my own. :)

oh if you want to try it on your own, don't click, although the picture may be helpful

\[\color\magenta\heartsuit\]

@misty1212 very good explanations!