## anonymous one year ago find any vertical asymptotes of the function limit of 1 divided by the quantity x minus 8 as x approaches 8 from the left

1. anonymous
2. anonymous

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

3. anonymous

yea.

4. anonymous

you know what it looks like?

5. anonymous

not exactly

6. anonymous

has a vertical asymptote at $$x=8$$ for sure

7. anonymous

did you graph these in some pre-calc class?

8. anonymous

this is for my final assignment for my online class

9. anonymous

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

10. anonymous

oh well if it is on line lets cheat like crazy

11. anonymous
12. anonymous

you and i would become good friends lol

13. anonymous

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

14. anonymous

you can see that from the picture right?

15. anonymous

yea

16. anonymous

ok my motto "cheating is learning"

17. anonymous

awesome. that is now my new motto

18. anonymous

19. anonymous

wait so is x=8 the only one?

20. anonymous

yes of course

21. anonymous

only place where the denominator would be zero

22. anonymous

ok thank you so much

23. anonymous

yw

24. anonymous

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

25. anonymous

ok one last question

26. anonymous

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

27. anonymous

lord i thought it as going to be a short one

28. anonymous

ok first the fifth root of 243 is 3 i think

29. anonymous

lol sorry.

30. anonymous

then divide $$240$$ by $$5$$

31. anonymous

i get 48

32. anonymous

that would be 48

33. anonymous

yea

34. anonymous

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

35. anonymous

next we add 360 to 240 and divide by 5 again

36. anonymous

ok so it would be 120

37. anonymous

$360+240=600,600\div 5=120$ right

38. anonymous

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

39. anonymous

lather, rinse, repeat

40. anonymous

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

41. anonymous

$600+360=960, 960\div 5=192$

42. anonymous

3(cos(192°)+isin(192°))

43. anonymous

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

44. anonymous

haha sorry

45. anonymous

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

46. anonymous

i will let you finish the last two $960+360$ etc

47. anonymous

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

48. anonymous

you are welcome, hope you pass