find the limit of (x+7)/(x^2 -6x + 9) as x approaches 3. please show all calc involved

Question

find the limit of (x+7)/(x^2 -6x + 9) as x  approaches 3. please show all calc involved

amistre64 · Answer

is 3 a bad value for x?

anonymous · Answer

what do you mean?

amistre64 · Answer

what makes a bad fraction?

anonymous · Answer

when i plug in 3, i get 10/0...thats not good according to my teacheelser but dont know what else to do

amistre64 · Answer

right, /0 is a bad fraction so x=3 makes this go bad

amistre64 · Answer

can we undo the offending part with algebra?$$\frac{(x+7)}{(x-3)^2}$$
prolly not

myininaya · Answer

lol
i love your definition of the term bad fraction
i like to say discontinuous at such and such but bad fraction is a good term

amistre64 · Answer

http://www.wolframalpha.com/input/?i=limit%7Bx+to+3%7D+%28x%2B7%29%2F%28x-3%29%5E2

myininaya · Answer

So anyways since there is no way to force this fraction to be continuous at x=3 then the limit does not exist

amistre64 · Answer

inf aint a good answer then is it :)

amistre64 · Answer

it aint a real number so ....

myininaya · Answer

does not exist is fine
but saying it approaches infinity gives a little more info on that "does not exist" phrase

anonymous · Answer

Infinty and does exists are not same right?

amistre64 · Answer

exist means a definitive value; infinity is more a direction than a value i believe

myininaya · Answer

right amistre

anonymous · Answer

This limit exists and it is infinity...

anonymous · Answer

what about x^2-x-20/2x^2-32, as x approaches -4

anonymous · Answer

happy birthday myininaya

myininaya · Answer

infinity is not a number

anonymous · Answer

Right hand limit =left hand limit = infinity

myininaya · Answer

so it does not exist

anonymous · Answer

I know but infinity is not same as undefined.

amistre64 · Answer

attachment

myininaya · Answer

infinity is fine to say when both sides are approaching infinity
(same for negative infinity)
but i feel it is also okay to say it dne since infinity is not a number

anonymous · Answer

amistre whats the screenshot for

anonymous · Answer

but can anyone help with the last question i posted please

myininaya · Answer

hes just saying the question in the window thingy is not the same as the question you asked

anonymous · Answer

For this question I would say that the limit is infinity, but if for the purposes of some questions where only finite limits are applicable then an infinite limit might be considered DNE.

zarkon · Answer

I'd probably say infinity too, but with the understanding that the limit really does not exist...infinity is just the direction that the function is going.

anonymous · Answer

Myin, this is interesting: http://math.stackexchange.com/questions/36289/