Thread: What functions fit these requirements..?

1. What functions fit these requirements..?

1) lim f(x) =2 where x->3 and f(3) exists

2) lim f(x) =2 where x->3 but f(3) does not exist

3) lim f(x) =2 where x->3 and is infinite (does not exist)

4) lim f(x) =2 where x->3- but lim f(x) where x->3+ does not exist

2. Originally Posted by yess
1) lim f(x) =2 where x->3 and f(3) exists

2) lim f(x) =2 where x->3 but f(3) does not exist

3) lim f(x) =2 where x->3 and is infinite (does not exist)

4) lim f(x) =2 where x->3- but lim f(x) where x->3+ does not exist
I recommend thinking graphically. I also recommend showing some work and saying where you got stuck.

3. Originally Posted by undefined
I recommend thinking graphically. I also recommend showing some work and saying where you got stuck.
the problem is i have noooo idea where to start!!

4. Originally Posted by yess
the problem is i have noooo idea where to start!!
Here's another idea then. Think of some common functions like f(x)=x. Does this function satisfy (1)? How about (2)?

5. for 1) i have f(x) = 3x + 3
is that ok??

6. Originally Posted by yess
for 1) i have f(x) = 3x + 3
is that ok??
Why would you think $\displaystyle \lim_{x\to3}(3x+3)=2$? It's way off.

Hint: For (1) just choose any function that is continuous everywhere and that satisfies f(3)=2.

(Note: What I wrote at first wasn't quite right, I edited it.)

7. Originally Posted by undefined
Why would you think $\displaystyle \lim_{x\to3}(3x+3)=2$? It's way off.

Hint: For (1) just choose any function that is defined everywhere and where f(3)=2.
ooooh it makes more sense looking at it like that!
soo maybe x-1 ??

8. Originally Posted by yess
ooooh it makes more sense looking at it like that!
soo maybe x-1 ??
Yep that works.

9. so i've got all but 2) .. any hints??

10. Originally Posted by yess
so i've got all but 2) .. any hints??
Draw the graph for f(x)=x-1 except that where x=3 draw a hollow circle..