Question

Find the limit if one exists. lim x approaches 6 x+6/(x-6)^2

Answer 1

\[\lim_{x \rightarrow 6}\frac{ x+6 }{ (x-6)^{2} }\]

Answer 2

@whpalmer4

Answer 3

just plug in x= 6 in that

Answer 4

But you get 0

Answer 5

that in the denominator, not in numerator also. numerator = 12, right ?
and whats anything positive/0 =.... ?

Answer 6

0...
BUT IT CAN'T BE THAT SIMPLE ? !
Don't you have to do other stuff...

Answer 7

@hartnn anything 0/x is 0 :)
x/0 is undefined

Answer 8

its not 0
(anything positive)/0 = +infinity!

Answer 9

oh wait
whops

Answer 10

omg

Answer 11

Oops too

Answer 12

and thats it! you don't need to do anything else...

Answer 13

so does DNE works ?

Answer 14

not undefined, here, it'll be +infinity

Answer 15

anything positive/0 = +infinity
anything negative/0 =-infinity

Answer 16

there;s not answer for that in the multiple choice tho

Answer 17

Here's a graph showing the approach from 5 and 7, should be clear that it gets big fast as you approach x = 6 :-)

Answer 18

its not DNE, when left hand limit does not equal right hand limit, then we say the limit DNE.
here, you are getting the limit as +infinity.

Answer 19

what are the choices ?

Answer 20

DNE, 6, -6, 0

Answer 21

Are you like barely learning limits?

Answer 22

yeah x__x

Answer 23

strange, none of them is correct....

Answer 24

OHHH whpalmer

Answer 25

Ah then I've had to deal with before.. it's DNE @hartnn

Answer 26

yeah, the limit is definitely \(+\infty\)

Answer 27

if i have to go with one, i'll go with DNE

Answer 28

They do not take/learn infinity for limits yet

Answer 29

Not till later at least

Answer 30

not enough time to do it/learn it right, but there will be time to do it over later, I guess...

Answer 31

hmm...go with DNE then

Answer 32

Yup, DNE

Answer 33

Wow ok thanks guise..
wait one more
a similar question

Answer 34

so i guess this one is also DNE ?

Answer 35

Try the conjugate first

Answer 36

Infinity is just convenience, isn't it?
I mean, an infinite limit... is no limit...

Answer 37

shouldn't that be
\(\sqrt x-\sqrt {49} \quad or \quad \sqrt x-7 ???\)

Answer 38

you can't just plug in the number
you have to change the equation so that the denominator is not equal to 0

Answer 39

and then you have to plug in 6

Answer 40

if the question posted is correct, then again just plug in x=49...

Answer 41

multiply by sqrt{x}+sqrt{49}

Answer 42

@musiklover317 you can, if the numerator is not also 0. it's the indeterminate forms where you have to apply L'Hopital.

Answer 43

but the numerator has sqrt 7 !
are you sure you copied the question correctly ??

Answer 44

so you get DNE again...
yeah it's the right question!

Answer 45

then yes, just plug in x=49

Answer 46

@hartnn can I show you my process?

Answer 47

interesting..

Answer 48

yes, Luigi, you can show us how we will reach to DNE in this case also

Answer 49

@whpalmer4 changing the equation will be the easiest and simplest way to think.

Answer 50

now this one is a legit DNE — the limit is different from each side.

Answer 51

@musiklover317 show us what you mean by solving it entirely by yourself..

Answer 52

oh hey the answer is infinity

Answer 53

right! +infinity for 1st and DNE for 2nd ...

Answer 54

@hartnn 's right

Answer 55

oh, we all are correct ;)

Answer 56

Haha @_@
Now i'm stuck on another question...
Evaulate or determine that the limit does not exist for each the limites
(a) lim x->d- f(x)
(b) lim x->d+ f(x)
(c) lim x->d f(x)
for the given dunction f and the number d

Answer 57

can you ask new question on every new post, please ?

Answer 58

OH LOL OK sorrie
do i post it now

Answer 59

@hartnn
You mean 'can you make a new post for every new question' right? :3

Answer 60

yeah, same thing, thanks!
and yes.