The discussion revolves around finding the limit of the expression (x^2-16)/(4-x) as x approaches 4. Participants are exploring the implications of factoring and simplifying the expression, particularly focusing on the behavior of the terms involved as they approach the limit.
The discussion is ongoing, with participants actively questioning each other's reasoning and attempting to clarify the mathematical relationships involved. There is no explicit consensus, but several lines of reasoning are being explored regarding the simplification process and the interpretation of the negative sign.
Participants are working within the constraints of a homework assignment, which may limit the information available for discussion. The nature of the problem involves limits, and there is an emphasis on understanding the algebraic manipulation of the expression.
What is -(x-4) ?Johnyi said:Homework Statement
Lim x^2-16/4-x
x→4
Homework Equations
The Attempt at a Solution
I factored it, and ended up with (x-4)(x+4)/(4-x)
Cant cancel anything out, so I plug in 4 back into it, and end up with 8 as the limit. But the book says that the answer is -8?
SammyS said:What is -(x-4) ?
SammyS said:What is -(x-4) ?
Why do you think it would be zero?Johnyi said:Wouldnt that just be 0? Also why is there a - before the (x-4)?
I'm not asking you to take the limit of -(x-4).SammyS said:What is -(x-4) ?
Don't worry about that until you answer the question I asked.Johnyi said:Where did you get the - before the (x-4) though?
SammyS said:Don't worry about that until you answer the question I asked.
It may be clear to you after that.
Almost correct.Johnyi said:So if i distribute the - it will be -x+4, which cancels with the denominator, and I am left with x+4. I plug in 4 for x and get 8?
SammyS said:Almost correct.
Yes, you're right about -(x-4) = -x + 4. Of course that is the same as 4 - x .
So rewrite your expression with a denominator of -(x - 4).
Do you see why I had the "-" sign out front of the (x-4) in my previous posts?
Didn't you determine that -(x-4) is -x + 4 ?Johnyi said:Sorry..I just can't understand how the "-" sign came out of nowhere, and why i have to rewrite the denominator as -(x-4)
If the denominator is -(x-4) then there is also a "-" sign left uncancelled.Johnyi said:So then wouldn't they both cancel anyways leaving me with just (x+4)?