Question

Find the indicated limit, if it exists.
lim x->2 {x+3 x< 2 }
{3-x x>_ 2}

Answer 1

Plug in \(x=2\) to both cases and see what happens.

Answer 2

@wio you get 5 and 1.

Answer 3

Do you know where I got \(2\) from?

Answer 4

the limit as x approaches 2?

Answer 5

Yes

Answer 6

But there is another reason as well, both cases are split on 2.

Answer 7

So we need to see if both cases approach 2 on both sides.

Answer 8

The limit only exists if both sides approach the same number. You can graph it to see as well.

Answer 9

how would you graph it?

Answer 10

so it DNE?

Answer 11

@wio

Answer 12

Yes

Answer 13

Does it make sense how I graph it?

Answer 14

Yea, can you help me with another one?

Answer 15

lim x-> 0 {5x-9 x<0}
{ l 2-x l x>_0}