How would I determine if a limit is undefined in Calculus?

Question

ganeshie8 · Answer

Consider the function f(x) = 1/x

ganeshie8 · Answer

Can you tell me the value that the function approaches as "x" approaches "0" ?

augustmae · Answer

I'm not sure I understand

ganeshie8 · Answer

Could you please be specific about what exactly you didn't understand ?

augustmae · Answer

I'm sorry, This is very new to me. I just started calculus so I didn't understand the question.

augustmae · Answer

One of the questions in my HW is: lim 4x^2/x + 2 as x tends to 2.  I got -6, but the answer said it was undefined.

ganeshie8 · Answer

x tends to 2

or

x tends to -2 ?

augustmae · Answer

x tends to positive 2

augustmae · Answer

I attached the equation:

augustmae · Answer

oh. negative -2.

augustmae · Answer

x tends to -2

augustmae · Answer

that might be my problem.

ganeshie8 · Answer

Plugin x = -2 in the given function
what do you get ?

augustmae · Answer

actually I did use -2. My answer was -6

ganeshie8 · Answer

How ?

ganeshie8 · Answer

Its

4x^2
-----
x+2


not

4x^2/x  +  2

augustmae · Answer

That's the answer I keep getting. 
4(-2)^2 / (-2)+2 = -6

ganeshie8 · Answer

Wrong.

ganeshie8 · Answer

Don't you see the difference between 

4x^2/(x+2)   

and

4x^2/x + 2

?

augustmae · Answer

I see it. -2+2 = 0 making it undefined.
Thanks you anyway

ganeshie8 · Answer

Exactly! I suggest you check with your teacher again on why the limit is undefined here

ganeshie8 · Answer