Question

How do you find one sided limits without using a table of value? I.e: Limit as x->3 on its left hand side (3-) of x^2 l x-3 l / x -3

Answer 1

Hello

Answer 2

Hi!

Answer 3

Now one sided limits are apllied when the function values behave differently when approaching the point from the left versus the right hand side

Answer 4

What is the very clear factor there that behaves differently ?

Answer 5

Meaning around the poiny x =3 - just to the left vs. just to the right ...

Answer 6

@MarcLeclair ?

Answer 7

but how do you end up solving it without using a table of value, I can manage to find the limits of the right hand side using a table of value, I can't work it out algebraically. Unless there is no way other than error and trial

Answer 8

You very easily will understand that u CAN algebraically - just answer my guiding question

Answer 9

What factor changes behaviour around x=3

Answer 10

The Y values? or is it that the function isn't continuous like piece wise functions or step functions?

Answer 11

It is continuous but it ALSO is kind-of piece-wise defined yes - two definition around 3

Answer 12

So the left hand side limit is different than the right hand side, lets just say at random numbers the right hand side is f(x) = 3 and left hand side is f(x)=10 (random values that i picked)

Answer 13

Marc please concentrate on my guiding question: WHAT ALGEBRAIC FACTOR CHANGES BEHAVIOR AROUND 3 ?

Answer 14

I can't tell you, any hint? I am trying to think but i really can't figure it out.

Answer 15

|x| = \[|t| = \left\{ t..... IF... t> 0 \right\}\]
\[|t| = -t ......IF... t<0\]

Answer 16

|x-3| = x-3 for x >3 AAand it changes to |x-3| = -(x-3) for x<3

Answer 17

SO it follows that when you divide by (x-3) factor then u get

Answer 18

Oh! I am so sorry I didn't find the question right away. So the limit changes at 3 because the absolute value makes it either + or -. Therefore, when removing the absolute value bracket , you are left with 2 options. either - (x -3 ) or (x +3 )

Answer 19

\[\frac{ (x-3) }{ x-3 } = 1\]

Answer 20

1 is on the right of course

Answer 21

so then you have to do the opposite so - (x -3) to get on the left hand side!

Answer 22

Aaand \[\frac{ -(x-3) }{ (x-3) } = -1\] on the left hand side

Answer 23

therefore it will give you - 1 and then you will end up with -9

Answer 24

thank you very much for your patience!

Answer 25

As they say in Kentucky : Yep, ya right on it

Answer 26

can i ask you another question on here really quickly?

Answer 27

click the blue ribbon "best response"

Answer 28

Ask

Answer 29

What if the question was without an absolute so lets say lim x-> -3 on the left hand side of x-3 / x+ 3.

I can't factor anything and the denominator makes me end up with 0. So the answer would be infinity?

Answer 30

NOO! Algebra IS allowed - algebraically your FRACTION is ODENTICALLY 1 everywhere except 3 where it is undefined (because of 0). But limit does not care about the single point. Limit of a constant 1 = 1

Answer 31

Thank you! :)