Question

Need help with a 2 sided limit question. Will post when i start question. Easier to use equation formatter

Answer 1

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

*graph supplied* http://postimg.org/image/d9s8oel7r/

\[\lim_{x \rightarrow 2-}\] and \[\lim_{x \rightarrow 2+}\]

Answer 2

the limit is the value you "approach" as x approaches (but *never* reaches) 2
from the left for 2- and from the right moving left to 2+

Answer 3

Alright. How do i use the graph to determine it?

Answer 4

your question left out a detail. I assume they want (for example)
\[ \lim_{x\rightarrow 2^-}\ f(x)\]

Answer 5

and f(x) is the value of the function i.e. the y value

Answer 6

Ah when typing the information in i forgot to input f(x) for each lim x-> 2- or lim x-> 2+

Answer 7

I assume you can read off f(0) from the graph ?

Answer 8

I think so

Answer 9

put your finger on 0 on the x-axis, move up until you reach the line. what y value are you at ?

Answer 10

positive 5

Answer 11

and what do you get for f(2-)
(by 2- I mean just a bit to the left of 2)

Answer 12

y is at 5
x would then be 1.9?

Answer 13

in theory x is at 1.999999999.... as many 9's as you want.
but you never "get" to the open circle at 2, so f(x) will be 5
f(x) is 5 until x gets to *exactly* 2, when f(2) is 1 (the black dot)

Answer 14

the idea is the limit of f(2-) is 5 (because limits *never* allow x to be 2, just to approach it)

Answer 15

now do f(2+)
which is the value of f at just a bit to the right of 2

Answer 16

2.0000000000000(you can keep going for ages)1

Answer 17

yes, but what is f at that x?

Answer 18

-2?

Answer 19

yes

that is the limit

Answer 20

Alright. So its two limits i put down? 5 and -2?
Thank you phi. you have been a huge help

Answer 21

yes

Answer 22

Sweet. going to close the question now. Have a good day