Question

Find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x.
Someone help??

Answer 1

Find the limit as x approaches 2 from the left.
that means put your finger to the left of 2 (say at x=1)
and let x get closer and closer to 2 (but *never* reach it)
what is the y value?

Answer 2

0? @phi

Answer 3

what is the y value at x=1?

Answer 4

4?

Answer 5

and y stays 4 as you move towards x=2

Answer 6

Ok so would my answers be:
As x approaches 2 from the left, the y-value is 4

As x approaches 2 from the right, the y-value is -4 ?

@phi

Answer 7

yes. The idea (of a limit) is we never let x get to 2, and look at what y is doing
as we move *very* close to x=2, y stays 4, and we say the limit is 4
(from the left)
and ditto for the right , except y is -4

Answer 8

Oh ok! So should I say the y-value is or the limit is?

Answer 9

the limit.
the actual y value at x=2 is y= 1 (based on the graph)

but the limit is something different.

Answer 10

Oh ok! Thanks so much!

Answer 11

you might wonder why we have such a strange idea as limit, but it turns out to be useful.