Question

find any vertical asymptotes of the function
limit of 1 divided by the quantity x minus 8 as x approaches 8 from the left

Answer 1

https://i.gyazo.com/600783c4843f253829c56f7ccc1a8a91.png

Answer 2

\[f(x)=\frac{1}{x-8}\]?

Answer 3

yea.

Answer 4

you know what it looks like?

Answer 5

not exactly

Answer 6

has a vertical asymptote at \(x=8\) for sure

Answer 7

did you graph these in some pre-calc class?

Answer 8

this is for my final assignment for my online class

Answer 9

actually we can cheat easily, do it without knowing the graph

Answer 10

oh well if it is on line lets cheat like crazy

Answer 11

http://www.wolframalpha.com/input/?i=1%2F%28x-8%29

Answer 12

you and i would become good friends lol

Answer 13

you can see that as \(x\to 8^-\) it goes to \(-\infty\)

Answer 14

you can see that from the picture right?

Answer 15

yea

Answer 16

ok
my motto "cheating is learning"

Answer 17

awesome. that is now my new motto

Answer 18

all rights reserved

Answer 19

wait so is x=8 the only one?

Answer 20

yes of course

Answer 21

only place where the denominator would be zero

Answer 22

ok thank you so much

Answer 23

yw

Answer 24

and is it ok if you can help me with one last question

Answer 25

ok one last question

Answer 26

Find the fifth roots of 243(cos 240° + i sin 240°)

Answer 27

lord i thought it as going to be a short one

Answer 28

ok first the fifth root of 243 is 3 i think

Answer 29

lol sorry.

Answer 30

then divide \(240\) by \(5\)

Answer 31

i get 48

Answer 32

that would be 48

Answer 33

yea

Answer 34

so one answer is \[ 3(\cos (48°) + i \sin (48°))\]

Answer 35

next we add 360 to 240 and divide by 5 again

Answer 36

ok so it would be 120

Answer 37

\[360+240=600,600\div 5=120\] right

Answer 38

so 2nd answer is \[3(\cos (120°) + i \sin (120°))\]

Answer 39

lather, rinse, repeat

Answer 40

alright. so once again i add 360 and divide by 5?

Answer 41

\[600+360=960, 960\div 5=192\]

Answer 42

3(cos(192°)+isin(192°))

Answer 43

third answer is \[3(\cos (192°) + i \sin (192°))\] you are too fast for me

Answer 44

haha sorry

Answer 45

no that is good, you get the picture, even though evidently you will never use this again

Answer 46

i will let you finish the last two \[960+360\] etc

Answer 47

ok thanks so much for the help. thats everything i needed help with

Answer 48

you are welcome, hope you pass