Question

I'm really confused on how to do this:
Find the indicated limit, if it exists.

limit of f of x as x approaches 5 where f of x equals 5 minus x when x is less than 5, 8 when x equals 5, and x plus 3 when x is greater than 5

Answer 1

please write it out, or draw it.

Answer 2

I think I can get it formatted :) One sec.

Answer 3

\[\Large\rm f(x)=\cases{5-x,&x < 5\\ \rm 8\qquad~,&x = 5\\ \rm x+3,&x > 5}\]So this is our f(x), yes?
Please don't look at my code, it's so sloppy lol

Answer 4

We don't actually care what the function equals AT x=5.
The limit tells us what happens as we get closer and closer, but not actually at the location.
So we'll ignore the middle piece.

Answer 5

When we approach from the left side,
\[\Large\rm \lim_{x\to5^-}f(x)=\lim_{x\to5^-}(5-x)\]
We use the branch of our piece-wise function that corresponds to where we are.

Answer 6

Evaluating the limit tells us that the function is approaching 0 from the left side.
Understand what I did there?
Do you think you can do the right sided limit?

Answer 7

0 and 8

Answer 8

@zepdrix

Answer 9

Is this the piece wise function?

Answer 10

so it would be dne bc 0 isn't equal to 8 right?

Answer 11

Yes, very good! :)
The limit from the left does not agree with the limit from the right.
So the limit of the function, as x approaches 5, does not exist.

Answer 12

thanks for the help :) and sorry i took long