Question

pre calc help =^.^=

Answer 1

Use graphs and tables to find the limit and identify any vertical asymptotes of the function.

Answer 2

basically to graph the function and determine the limit using the numerical approach.

Answer 3

lim 1/x-10
x-10^-

Answer 4

\(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~10^{-}}~\frac{1}{x-10}}\) like this?

Answer 5

yup

Answer 6

i know that the vertical asymptote is 10 correct

Answer 7

yes vertical asymptote is x=10.

Answer 8

ok now i am having trouble finding the limit

Answer 9

now, please give me some examples of numbers that are close to 10 "from the left"

Answer 10

1-9?

Answer 11

I would say 9 , 9.1 , 9.44 , 9.75 etc...

Answer 12

ok

Answer 13

some values that are less than 10.

but for precision lets use 9.9 9.99 9.999 9.9999 and etc...

Answer 14

ok

Answer 15

\(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~10^{-}}~\frac{1}{x-10}}\)

at x=9 , \(\large\color{slate}{\displaystyle~\frac{1}{9-10}=\frac{1}{-1}=-1}\)

at x=9.9 , \(\large\color{slate}{\displaystyle~\frac{1}{9.9-10}=\frac{1}{-0.1}=-10}\)

at x=9.99 , \(\large\color{slate}{\displaystyle~\frac{1}{9.99-10}=\frac{1}{-0.01}=-100}\)

Answer 16

now try plugging in
`9.999`
and
`9.9999`
and on yourself for 2 or 3 times

Answer 17

ok sec

Answer 18

wait you lost me...
oh wait nvm u plauged in the 9.... for x.... correct?

Answer 19

yes I plugged in values that closer and closer approach 10 from the left.

when I say from the left I mean

Answer 20

ok i see

Answer 21

so then what wuld i write as my limit...?

Answer 22

(I will repost the last post about plugging in x values)

Answer 23

\(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~10^{-}}~\frac{1}{x-10}}\)

at x=9 , \(\large\color{slate}{\displaystyle~\frac{1}{9-10}=\frac{1}{-1}=-1}\)

at x=9.9 , \(\large\color{slate}{\displaystyle~\frac{1}{9.9-10}=\frac{1}{-0.1}=-10}\)

at x=9.99 , \(\large\color{slate}{\displaystyle~\frac{1}{9.99-10}=\frac{1}{-0.01}=-100}\)

Answer 24

\(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~10^{-}}~\frac{1}{x-10}}\)

at x=9.999 , \(\large\color{slate}{\displaystyle~\frac{1}{9.999-10}=\frac{1}{-0.001}=-1000 }\)

at x=9.9999 , \(\large\color{slate}{\displaystyle~\frac{1}{9.9999-10}=\frac{1}{-0.0001}=-10000 }\)

at x=9.99999 , \(\large\color{slate}{\displaystyle~\frac{1}{9.99999-10}=\frac{1}{-0.00001}=-100000 }\)

Answer 25

see, that as I am getting closer to zero, the bigger the value gets

Answer 26

yea

Answer 27

I mean the smaller, the more it tends towards \(-\infty\)

Answer 28

so then the limmit is 0.. or 10?

Answer 29

i am a little confused :/

Answer 30

i get that the closer we get to ten the more percise it becomes... but then you made it into 0.01

Answer 31

so id the limit 10 or 0?

Answer 32

or are they both limits?

Answer 33

no if the closer you get to 10 the more your value tends to \(-\infty\).

THAT MEANS that the limit is equivalent to \(-\infty\)

or, technically speaking: The limit does not exist, it diverges to \(-\infty\).

Answer 34

so when i where to write it would i write -infinity or "doesnt exist"?

Answer 35

it is -infinity and that means it doesn't exist.

Answer 36

when the limit is -infinity, then it doesn't exist, because it is not approaching a particular value.

Answer 37

ahh ok thank you :)

Answer 38

yw