Question

lim x--> 3 x-3 / 2x^2 - 9x - 9

Answer 1

wait

Answer 2

i would attempt to factor the denominator

Answer 3

then see if any factors cancel

Answer 4

or just plug in 3 and see if you need to do that

Answer 5

if you get 0/0 you need to
if you don't then you are done

Answer 6

Just plug in 3

Answer 7

\(\large\color{black}{\displaystyle\lim_{x \rightarrow ~3}~~\frac{x-3}{2x^2 - 9x - 9}}\)

Answer 8

I am confused ... I do not understand what you are saying .. :(

Answer 9

you have \(\large\color{black}{\displaystyle\lim_{x \rightarrow ~3}~~\frac{x-3}{2x^2 - 9x - 9}}\) and you are able to just plug in 3 for x, without doing anything, because when x=3, the denominator is NOT zero.

Answer 10

can you tell me what you get after plugging in x=3?

Answer 11

yes hold on

Answer 12

sure

Answer 13

do I plug in 3 to the top and bottom or only the denominator?

Answer 14

you plug in three for x, into the top and the bottom.

Answer 15

\(\large\color{black}{\displaystyle\lim_{x \rightarrow ~3}~~\frac{x-3}{2x^2 - 9x - 9}=\frac{(3)-3}{2(3)^2 - 9(3) - 9}}\) like this

Answer 16

i got 0

Answer 17

yes.

Answer 18

it is 0/-18 which is same as just 0.

Answer 19

yeah

Answer 20

good work!

Answer 21

but that is all I do ? don't I have to get a number before and after 3 and plug it in to see what the limity as x approaches 3 is?

Answer 22

u get a medal @SolomonZelman

Answer 23

limit*

Answer 24

I didn't do anything

Answer 25

@ilovereyvis_x3 some other questions?

Answer 26

btw do you want to know how I am putting up this in latex?

Answer 27

my teacher doesn't do that , she never plugs in the number she finds a number before and after that number to find the limit as it approaches that certain number ... do you know what I am talking about?

Answer 28

what does your teacher do, she factors or does other techniques to find the limit?

(I mean in this case, since there is no restriction for x to equal 3. you CAN just plug in 3 for x. This is the correct way to do it.)

Answer 29

numerical approach?

Answer 30

I am not sure what she calls it , it is weird , for example for this one we are finding the limit as x approaches 3 so she would use -2.9 and 3.1 or any number before or after the number 3

Answer 31

ohh she is just filling in the table of values

Answer 32

that is called a numerical approach
but usually more numbers are chosen to the left for left limit
and usually more numbers are chosen to the right for right limit

(you know instead of just one)

Answer 33

lets say x is approaching 3. So she fills in values of that limit as x approach 3 from the left.
values like

x=2.5
x=2.9
x=2.99
x=2.999

plugging these values and seeing what the limit approaches from the left side.

and from the right side she does.

x=3.5
x=3.1
x=3.01
x=3.001

Answer 34

like a big table of values

Answer 35

I am not sure I am going to attach my notes so you can see a visual example of what I do in my class

Answer 36

I know what approach you are taking about.

Answer 37

see my big reply above?

Answer 38

yes exactly like that !

Answer 39

that is what she wants us to show as work

Answer 40

yes, so we could have done it like if you want to. But once we have actually found the limit, it wouldn't make a difference what approach to use.

We can still make a table if you want to.

Answer 41

can you slow down please

Answer 42

those are the notes

Answer 43

yes, okay and what would you like to know?>

Answer 44

how can I do the problem the way she wants it so I can understand it and get full credit because I have 6 problems to do with limits for this winter packet she gave me

Answer 45

you have to estimate the limit.
for example when x is approaching 4 of f(x) make 2 tables.

left side right side
\(\normalsize\color{ black }{\LARGE{\bbox[5pt, lightyellow ,border:2px solid white ]{ \huge{ \begin{array}{| l | c | r |}
\hline \scr~~~x~~ & \scr f(x) \\
\hline
\scr~~~3.5~ & \scr ~~~ \\
\hline
\scr~~~3.7~ & \scr ~~~ \\
\hline
\scr~~~3.9~ & \scr ~~~ \\
\hline
\scr~~~3.99~ & \scr ~~ \\
\hline \scr~~~3.999~ & \scr ~~ \\
\hline \end{array} }}}}\) \(\normalsize\color{ black }{\LARGE{\bbox[5pt, lightyellow ,border:2px solid white ]{ \huge{ \begin{array}{| l | c | r |}
\hline \scr~~~x~~ & \scr f(x) \\
\hline
\scr~~~4.5~ & \scr ~~ \\
\hline
\scr~~~4.3~ & \scr 3 \\
\hline
\scr~~~4.1~ & \scr 4 \\
\hline
\scr~~~4.01~ & \scr 5 \\
\hline
\scr~~~4.001~ & \scr 5 \\
\hline \end{array} }}}}\)

Answer 46

oops, they didn't fit.

the bottom chart is for the right side, the top chart is for the left side.

Answer 47

and any values of f(x) that are there disregard them

Answer 48

See the Xs that I am plugging in?

Answer 49

so I plug those numbers in as x ?

Answer 50

not necessarily those. it is your choice what to plug in for x, unless you are given specific numbers to plug.

Answer 51

Ok so I just need to pick one from the right and one from the left , which ones do you think will be best ?

Answer 52

But you see that in both of my tables the x was getting closer and closer to 4.
I could have made the charts smaller, apologize for thyat.

Answer 53

for example if they say find the limit as x approaches 0 she would use 0.1 and -0.1

Answer 54

yeah i see that

Answer 55

so for this one I can use 2.9 and 3.5 ?

Answer 56

yes, but the numbers in both of the tables have to be the same distance from 3 (if x is approaching 3)

Answer 57

ok , so then which ones do you think I should use ?

Answer 58

Considering a case where \(\large\color{black}{\displaystyle\lim_{x \rightarrow ~0}f(x)}\).
(any f(x) )

left side right side

\(\large\color{black}{ \large{ \begin{array}{| l | c | r |}
\hline \scr~~~x~~ & \scr f(x) \\
\hline
\scr-1 & \scr \\
\hline
\scr-0.5 & \scr \\
\hline
\scr-0.1 & \scr \\
\hline
\scr-0.05 & \scr \\
\hline
\scr-0.01 & \scr \\
\hline
\scr-0.001 & \scr \\
\hline \end{array} } }\) \(\large\color{black}{ \large{ \begin{array}{| l | c | r |}
\hline \scr~~~x~~ & \scr f(x) \\
\hline
\scr1 & \scr \\
\hline
\scr0.5 & \scr \\
\hline
\scr0.1 & \scr \\
\hline
\scr0.05 & \scr \\
\hline
\scr0.01 & \scr \\
\hline
\scr0.001 & \scr \\
\hline \end{array} } }\)

Answer 59

I am not filling in the f(x) values, but just showing how I set up the X values for each side.
they are away from the zero the same amount, the same distance.

like -0.05 is just as far from 0 as 0.05 is.

Answer 60

yeah for that case I use -0.1 and 0.1

Answer 61

yeah

Answer 62

I see what your saying , so if I use 2.9 I would have to use -2.9

Answer 63

I think ...

Answer 64

but it it is

Considering a case where \(\large\color{black}{\displaystyle\lim_{x \rightarrow ~2}f(x)}\).
(any f(x) )

left side right side

\(\large\color{black}{ \large{ \begin{array}{| l | c | r |}
\hline \scr~~~x~~ & \scr f(x) \\
\hline
\scr3 & \scr \\
\hline
\scr2.5 & \scr \\
\hline
\scr2.1 & \scr \\
\hline
\scr2.05 & \scr \\
\hline
\scr2.01 & \scr \\
\hline
\scr2.001 & \scr \\
\hline \end{array} } }\) \(\large\color{black}{ \large{ \begin{array}{| l | c | r |}
\hline \scr~~~x~~ & \scr f(x) \\
\hline
\scr1 & \scr \\
\hline
\scr1.5 & \scr \\
\hline
\scr1.9 & \scr \\
\hline
\scr1.95 & \scr \\
\hline
\scr1.99 & \scr \\
\hline
\scr1.999 & \scr \\
\hline \end{array} } }\)

Answer 65

I mean the first table is rigth side and the second table is left side. sorry

Answer 66

I have to leave for a second

Answer 67

don't worry I got it , thank you for your help !

Answer 68

you got it, sure? (I am back)