Question

assume that f(x) is everywhere continuous and it is given to you that f(2)=-7 and
lim (f(x)+7)/(x-2)=8
x➟ 2

it follows that y = ?

I dont really understand how to solve this question as if you were to directly sub in x=2 then you get a zero on top which would leave the left side equal to 0/0=8? normally in other questions you would factor but with this you cant factor it.

thanks for any help

Answer 1

Given that the limit is 8, we really do need 0/0, otherwise the fraction goes to ∞. So y = -7. So, if f(2) is anything but -7, such as 3, then we have 10/0 which = ∞ -- but we are told that the limit is 8.

But they just told us that f(-2) = -7. So why ask what y is? Isn't y=f(x)?

Answer 2

assuming no miscommunication, this question is incredibly confusing. i think that what it might be asking is not the limit but what would make it equal to 8? so I would just plug in random numbers till I get the limit = 8

Answer 3

it is confusing. But since the limit is a finite value, the fraction must be 0/0. For, if 0/0 = n, then that means that 0 = n*0. But that is true for <b>any</b> finite n. So if they tell you that the limit is 8, the fraction <b>must</b> be 0/0, since the bottom is zero.