Question

Could someone help me figure out these limits on the graph? Don't understand how to do it. Will attach pic.

Answer 1

I don't understand how to calculate the limit with the graph.

Answer 2

Its tedious looking at it from the picture.

Answer 3

hehehl, the picture is "viewable", but can't see the "subscript" for the number "x" is going to

Answer 4

Omg, I hated pre-calculus in HS.

Answer 5

Right, very small...but in general....say for example it says \[\lim_{x \rightarrow 2^+}\]

meaning limit as x approaches 2 from the right (positive) side

that means....look at your graph.....starting from the RIGHT side of the x axis (a.k.a numbers BIGGER than 2) and go down to the number 2 on the x-axis....now look at the graphed function....what value does it look like it has?

*hint* it CAN be different if say it was \[\lim_{x \rightarrow 2^-}\]

meaning limit as x approaches x from the left (negative) side

Answer 6

edit in that last sentence **limit as x approaches 2 from the left (negative) side

Answer 7

for example, say a) \(\large
x\rightarrow 0^-
\)

what do you think? @LucyLu15

Answer 8

@jdoe0001 it wouldnt exist?

Answer 9

so, why it doesn't exist?

Answer 10

it wouldnt exist because it has no point?

Answer 11

hehe
what does \(\large
x\rightarrow 0^-
\) stand for?

Answer 12

x approaching 0 from the left side.

Answer 13

just think about it like this........follow the lines in the function from the left side until you get to x = 0 ....what does it look like the line is equal to?

Answer 14

right, so let's look at "x" when it's less than 0, say -9/10, -8/10, -5/10, -2/10, -1/10, -1/100, -1/1000

do they exist?

Answer 15

they do not?

Answer 16

look at the graph :|

Answer 17

looks like a solid line from -9/10 to -1/100000

Answer 18

solid and continuos I'd say

Answer 19

yes, I see that.

Answer 20

so :)

Answer 21

wouldn't be the same for 0 approaching from the right? and then 0 as x approaches 0?

Answer 22

no, "limits" have a direction, when you go to the "left", you don't pay attention to the "right", and the other way around

Answer 23

I'd say when you go FROM the left, you don't pay attention to the right
or
you only focus forward

Answer 24

you don't look BEHIND per se :)