Question

Please help! AP problem test tomorrow! (image attached)

Answer 1

The key to this is to think about the left and right limits for each one of those, and what the sign ends up being.

Answer 2

I'm guessing answer E. If you plug in 3 for x and and subtract 3 you get 0 on the top and u subtract 3 on the bottom you got. 0 divided by 0 is undefined. I hope that helps.

Answer 3

^ That is what I thought. I'm not sure how to find the limit when the bottom would be negative or positive if I took the right and left hand limit.

Answer 4

E is actually true, not false. Here's why:
On the left of x, f(x)-f(3) is negative, and x-3 is negative, so you get -1.
On the right side of x, f(x)-f(3) is negtive, and x-3 is positive, so you get +1.

Answer 5

Oh, flip those answers haha. Left limit is +1. Right limit is -1.

Answer 6

o we're looking for false my bad i thought we were looking for true

Answer 7

didn't read the question carefully

Answer 8

Marvin, your method also doesn't work. You can't simply plug in, get 0/0 and decide that the limit is undefined.

Answer 9

What about the ones with an x in the denominator?

Answer 10

For example, consider
\[\lim_{x \rightarrow 0} \frac{x}{x}\]

Answer 11

I suggest you show him the correct method because my answer was a guess based on what I know.

Answer 12

That would be 1, yes?

Answer 13

Right.

Answer 14

And most of these are actually quite similar to that limit, but I just have to check the sign. pos/pos, neg/pos, neg/neg
etc.
Make sure that you don't get +1 from one side and -1 from another.

Answer 15

How do I evaluate the top part if I don't have the function? I just used l'hopital's rule for the bottom, but for it to work for the top I need to first know the function.

Answer 16

Just look at the graph and think about what the top part approaches. Any specific letter you're lookin' at?

Answer 17

By bad, the reason it wasn't working was because I was looking at B, which is the false one. Thanks!

Answer 18

=)