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

- anonymous

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- anonymous

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

- anonymous

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

- anonymous

yea.

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## More answers

- anonymous

you know what it looks like?

- anonymous

not exactly

- anonymous

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

- anonymous

did you graph these in some pre-calc class?

- anonymous

this is for my final assignment for my online class

- anonymous

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

- anonymous

oh well if it is on line lets cheat like crazy

- anonymous

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

- anonymous

you and i would become good friends lol

- anonymous

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

- anonymous

you can see that from the picture right?

- anonymous

yea

- anonymous

ok
my motto "cheating is learning"

- anonymous

awesome. that is now my new motto

- anonymous

all rights reserved

- anonymous

wait so is x=8 the only one?

- anonymous

yes of course

- anonymous

only place where the denominator would be zero

- anonymous

ok thank you so much

- anonymous

yw

- anonymous

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

- anonymous

ok one last question

- anonymous

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

- anonymous

lord i thought it as going to be a short one

- anonymous

ok first the fifth root of 243 is 3 i think

- anonymous

lol sorry.

- anonymous

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

- anonymous

i get 48

- anonymous

that would be 48

- anonymous

yea

- anonymous

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

- anonymous

next we add 360 to 240 and divide by 5 again

- anonymous

ok so it would be 120

- anonymous

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

- anonymous

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

- anonymous

lather, rinse, repeat

- anonymous

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

- anonymous

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

- anonymous

3(cos(192°)+isin(192°))

- anonymous

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

- anonymous

haha sorry

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

you are welcome, hope you pass

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