Question

My question is in regards to number 3 on the below picture. The book wants me to find the points of continuity and the points of discontinuity of the function and to identify each type of discontinuity. My question is how am I supposed to do #3 with limits?

Answer 1

Wait the pic was messed up

Answer 2

ok

Answer 3

This one is better

Answer 4

What grade are you in?

Answer 5

11th. AP Calc BC

Answer 6

Ok

Answer 7

Does the pic work?

Answer 8

yeah

Answer 9

Ok. Now how to do it...

Answer 10

@jim_thompson5910

Answer 11

Wait one sec :T

Answer 12

Ok, thanks!!!

Answer 13

Np lol

Answer 14

I gtg for like an hour.

Answer 15

okm

Answer 16

Ok, I'm back

Answer 17

What do you already know about limits?

Answer 18

?

Answer 19

A lot?

Answer 20

I don't know how to prove that this function is continuous. Thats the issue.

Answer 21

ok

Answer 22

@jim_thompson5910

Answer 23

I can't open that file

Answer 24

Ok well it says

Answer 25

Most people don't download files from students :/

Answer 26

y=(1)/(x^2+1)

Answer 27

can the denominator ever be equal to zero?

Answer 28

ie, are there any solutions to x^2 + 1 = 0 ?

Answer 29

Well excluding imaginary numbers, no

Answer 30

so there are no real numbered values that you can plug into x to make x^2 + 1 = 0 true

that means there is no possible way to divide by zero

Answer 31

Yes

Answer 32

visually this makes a graph with no discontinuities

Answer 33

I know this, but I need to use limits

Answer 34

there are no excluded values from the domain

Answer 35

So there isn't a way to really prove this?

Answer 36

that's the only way I can think of

Answer 37

Ok, thanks for the help!

Answer 38

sure thing

Answer 39

Srry I couldn't help you WaffleMan You're really smart Jim