Question

Use the given graph to determine the limit, if it exists.

Answer 1

\[\lim_{x \rightarrow 3-}f(x)\]

Answer 2

@paki @zzr0ck3r @SithsAndGiggles

Answer 3

So, because there is a jump continuous function, approaching from left or right will give the same value on x=3 because it is defined on the jump.
\[\lim_{x\rightarrow 3-} f(x)=7\]
\[\lim_{x\rightarrow 3+}f(x)=7\]
hence
\[\lim_{x\rightarrow3}f(x) =7\]
you might find the following link helpful
http://www.millersville.edu/~bikenaga/calculus/limlr/limlr.html

Answer 4

So, I was wrong above, kinda forgot the notation when I wrote it. the lim will be where the function jumps and not on the jump

Answer 5

So, approaching from the right, the function is linear at x=-4
so that is going to be the right hand limit

Answer 6

from the left it would be -1

Answer 7

Sorry, i was on the phone

Answer 8

so how would I write that out?

Answer 9

so, I messed up my right and left answers when I re-anwsered lol I havent done these in forever,
\[\lim_{x\rightarrow3-}f(x)=-1\]

Answer 10

you can solve by looking at the graph, if you have to show algebraic work, make an equation for the approach side, and the solve it at the value

Answer 11

so would it be
\[\lim_{x \rightarrow 3-}f(x)=-1\]
\[\lim_{x \rightarrow 3+}f(x)=-4\]

Answer 12

right.

Answer 13

what would i do with the 7

Answer 14

it looks likes that first one comes closer to the -2 marker
maybe i need to zoom in lol

Answer 15

zommed in , -1

Answer 16

i can't tell if it is above -2

Answer 17

at f(3) the function is that jump value, but the limits arent equal so the lim as x->3 is indeterminate because it isnt contiuous at that sight

Answer 18

its at -1 and -4 :p

Answer 19

sight = site, and this is if I'm remember this correctly.

Answer 20

so is there a limit or no?

Answer 21

for there to be a limit the left limit and right limit must be the same number

Answer 22

and since they aren't the same number, there is no limit?

Answer 23

yep again for the actual limit to exist the left limit and the right limit must be the same number

Answer 24

ok thank you all :)