Question

Find the indicated limit, if it exists.

Answer 1

Its right behind you!

Answer 2

all you need to do here is plug in -1 to each expression and make sure they are the same

Answer 3

So 4-x = 4-1 = 3

Answer 4

note: this one is pretty easy because each expression in the piecewise function is defined at x=-1
what we are doing is checking the limit at each endpoint and making sure they are the same.

it just happens that it is very easy to check the limit of the endpoints for this function, you just plug in -1

Answer 5

we are not looking at 1, we are looking at -1

Answer 6

4-(-1) = 5+1 = 5

Answer 7

we dont need to check the middle one, because it does not matter.

Answer 8

for a limit to exist we only care about the areas around the point, not the point itself

Answer 9

and x+6 = -1 + = 5

Answer 10

yep, so. as we approach -1 from the left we get 5, as we approach -1 from the right we get 5, so the limit is 5

Answer 11

Thank you, do you mind going through four more problems with me?

Answer 12

one more, but this was supposed to be my last. I got to get up in 7 hours:)

Answer 13

Okay, thank you and my apologies.

Answer 14

lol its fine:0

Answer 15

Use graphs and tables to find the limit and identify any vertical asymptotes of

Answer 16

ok do you have the thing graphed?

Answer 17

@Loveiskey18 ?

Answer 18

No, I'm attempting to graph it now.

Answer 19

http://www.wolframalpha.com/input/?i=1%2F%28x-4%29

Answer 20

Okay

Answer 21

what y value are we getting if we approach 4 from the left?

Answer 22

I got this http://www.wolframalpha.com/input/?i=lim&a=*C.lim-_*Calculator.dflt-&f2=(1)%2F(x-4)&f=Limit.limitfunction%5Cu005f(1)%2F(x-4)&f3=-+4&f=Limit.limit_-+4&a=*FVarOpt.1-_**-.***Limit.limitvariable--.**Limit.direction--.**Limit.limitvariable2-.*Limit.limit2-.*Limit.direction2---.*--

Answer 23

you looked at -4

Answer 24

do you just want the answer or to do the problem?

Answer 25

The y value is 4^1, right?
I want the answer, and the steps it took to get it. If you don't mind

Answer 26

ok then look at the graph I posted

Answer 27

as our x values get really close to 4 ( coming from the left) what is the graph doing?

Answer 28

It is curving downards.

Answer 29

we know the thing is undefined at x =4, so when we get close to 4 the thing is either shooting off to negative infinite or positive infinity

Answer 30

which do you think it is?

Answer 31

I honestly want to say negative.

Answer 32

yep

Answer 33

so, you just found the limit using the graph

Answer 34

So the answer is - (infinite sign) x = 4?

Answer 35

\[-\infty\]

Answer 36

yes.

Answer 37

\[\lim_{x\rightarrow 4^{-}}\frac{1}{x-4}=-\infty\]

Answer 38

now to solve this with a table we just plug in values for x that are really close to 4(coming from the left)

so let x = 3.9, 3.99, 3.99999, 3.999999999999999999
and you will see that its tending to negative infinity

Answer 39

do you know that the asymptote is?

Answer 40

the answer I posted.

Answer 41

@zzr0ck3r

Answer 42

I think you need to go back and study some old stuff. this is just going to get more confusing. you should know what an asymptote is if you are in calculus.

Answer 43

google it. hint...its x = something
its a number, not -infinitu

Answer 44

I know what it is, I asked you if -∞ ; x = 4 was the correct answer.

Answer 45

Well these are my options.

∞ ; x = -4

-∞ ; x = -4

-∞ ; x = 4

1 ; no vertical asymptotes