## anonymous 4 years ago lim x>4- ([[x]]-7)

1. anonymous

$\lim_{x \rightarrow 4-} ([[x]] -7)$

2. anonymous

greatest integer function, it will be a horizontal line from (3<=x<4)

3. anonymous

yea i have seen graphs of these functions

4. anonymous

looks sorta like steps

5. anonymous

yes

6. anonymous

but i have no idea how to graph one myself

7. anonymous

i am assuming if I graphed this I could see the limit

8. anonymous

which according to the book is 8

9. anonymous

You're approaching x=4 from the left, correct?

10. anonymous

they need a grapher on this site

11. anonymous

yes from the left

12. anonymous

If you're approaching 4 from the left, [[x]] will be 3

13. anonymous

so how to i determine the points i need to plot on [[x]]-7

14. anonymous

you have to take into account the -7

15. anonymous

yes, so -4 overall

16. anonymous

It's just the graph of f(x)=[[x]] shifted down 7 units

17. anonymous

well the book says 8 so .... >.<

18. anonymous

oh i know why

19. anonymous

i missed a 5 lol

20. anonymous

5[[x]]-7

21. anonymous

so to graph this

22. anonymous

yes, so 5(3)-7=8

23. anonymous

If you were approaching from the right, [[x]] would be 4

24. anonymous

25. anonymous

so you don't know how to graph the greatest integer function?

26. anonymous

nope i dont

27. anonymous

i know what they look like

28. anonymous

but not how to graph one given an equation

29. anonymous

|dw:1329178784965:dw|

30. anonymous

that is f(x)=[[x]]

31. anonymous

for 0-3

32. anonymous

yea how do i know to start at 0 and stop 1

33. anonymous

then start at 1,2 and stop at 2,1

34. anonymous

oops 1,1

35. anonymous

greatest integer function definition, [[x]] is the greatest integer less than or equal to x

36. anonymous

f(x)=[[x]] f(3.999999999999999999999)=3 f(3)=3 f(4)=4

37. anonymous

so by definition if x=1 then [[x]] is x>= 1

38. anonymous

i mean <=1

39. anonymous

if x=1, [[x]]=1

40. anonymous

Just think of it as going down the steps instead of up...you'll start as close as you can to [[x]]+1 and end up at [[x]]

41. anonymous

but you're not actually starting at [[x]] + 1

42. anonymous

so an open circle

43. anonymous

it is defined at all integers, but not continuous at any integer

44. anonymous

so if I were doing 5[[4]]-7 i would plot from (4,13) t0 (5,13) with an open point at (5,13)?

45. anonymous

yes, open circle at (5,13), closed at (4,13)

46. anonymous

and if it happened to be [[-x]] i would just reflect

47. anonymous

across the y axis, yes

48. anonymous

thanks

49. anonymous

np