Question

Directions: Complete the table and use the result to estimate the limit.
The limit as x approaches 4 is (x-4)/(x^2-3x-4)
x|3.9|3.99|3.999|4.001|4.01|4.1
f(x)| | | | | |

I don't even remember what a limit is or what any of this means so please be thorough in your response. Thanks!!

Answer 1

Hey Mads!

Small typo here, we're taking the limit `of` a function.
The limit as x approaches 4 of* (x-4)/(x^2-3x-4)

Answer 2

Calculator will be helpful here.
Here is our function,\[\large\rm f(\color{orangered}{x})=\frac{\color{orangered}{x}-4}{(\color{orangered}{x}^2-3\color{orangered}{x}-4)}\]So what is our result when we plug x=3.9 into the function?\[\large\rm f(\color{orangered}{3.9})=\frac{\color{orangered}{3.9}-4}{(\color{orangered}{3.9}^2-3\color{orangered}{(3.9)}-4)}\]

Answer 3

So I did that differently, just graphed it and then went to those points, although the answers are the same. I'm not sure how I know what the limit is though. Or really what is means. Most definitions really confuse me. All I know is that it's something a something approaches x but I don't get what that actually means.

Answer 4

Well with each point, our x is getting closer to 4.
Your y should be getting closer to some value.
That is the limit, the y value.

Answer 5

So the limit would be 0.2?

Answer 6

Yes.