Question

Can someone please, PLEASE, help me. I'm so tired of getting these questions wrong, I'm going insane and the lessons don't explain anything, please, can someone just help me?!

Answer 1

a limit exists if you get the same limit when x approaches 0 from above or below.

Answer 2

when x<0 (i.e. negative)
we use the first line
f(x)=5x-8

now when x is negative but *very* close to 0, we see f(x) will get *very* close to -8
Does that make sense ?

Answer 3

Barely...

Answer 4

x is negative and *very* close to zero. For example,
-0.00000000001

that is close to zero
now figure out
f(x) = 5x-8
= 5*-0.00000000001 -8 = -8.00000000005
which is very close to -8

Answer 5

most people (I think) "cheat" and say: if x were 0, we would get 5*0-8 = -8
of course, x is never allowed to get to 0, but it is allowed to get so close that practically speaking, the answer we get is very close to the answer we get using x exactly 0

Answer 6

So my answer should be -8?

Answer 7

that is the left hand limit
now you need to figure out the right hand limit (when x is above zero i.e. positive)
and approaches 0 from above.
notice when x is 0 or bigger we use the second line
f(x)= | -4-x |

Answer 8

I have no idea.

Answer 9

can you figure out f(0) using
f(x)= | -4-x |
?

Answer 10

|-4-0|

Answer 11

4?

Answer 12

inside the absolute value signs you have -4 - 0 which is -4
absolute value means make the answer positive, you get 4

so as x gets close to 0 (from the right)
f(x) gets close to +4

notice we have two different answers for the limit as x->0
depending on if x is neg or pos.
so we do *not* have a limit.

Answer 13

if you need more background, Khan has some good videos
Here is the first one
http://www.khanacademy.org/math/differential-calculus/limits_topic/limits_tutorial/v/introduction-to-limits--hd
or these (his early ones, which I like)
http://www.khanacademy.org/math/differential-calculus/limits_topic/old-limits-tutorial/v/introduction-to-limits

Answer 14

Can you tell me if I'm right in one of my other questions? I'll open a new post so I can give you a medal for it. c: