ChrisV 3 years ago lim x>4- ([[x]]-7)

1. ChrisV

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

2. rickjbr

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

3. ChrisV

yea i have seen graphs of these functions

4. ChrisV

looks sorta like steps

5. rickjbr

yes

6. ChrisV

but i have no idea how to graph one myself

7. ChrisV

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

8. ChrisV

which according to the book is 8

9. rickjbr

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

10. ChrisV

they need a grapher on this site

11. ChrisV

yes from the left

12. rickjbr

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

13. ChrisV

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

14. ChrisV

you have to take into account the -7

15. rickjbr

yes, so -4 overall

16. rickjbr

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

17. ChrisV

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

18. ChrisV

oh i know why

19. ChrisV

i missed a 5 lol

20. ChrisV

5[[x]]-7

21. ChrisV

so to graph this

22. rickjbr

yes, so 5(3)-7=8

23. rickjbr

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

24. ChrisV

25. rickjbr

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

26. ChrisV

nope i dont

27. ChrisV

i know what they look like

28. ChrisV

but not how to graph one given an equation

29. rickjbr

|dw:1329178784965:dw|

30. rickjbr

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

31. rickjbr

for 0-3

32. ChrisV

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

33. ChrisV

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

34. ChrisV

oops 1,1

35. rickjbr

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

36. rickjbr

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

37. ChrisV

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

38. ChrisV

i mean <=1

39. rickjbr

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

40. rickjbr

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. rickjbr

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

42. rickjbr

so an open circle

43. rickjbr

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

44. ChrisV

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. rickjbr

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

46. ChrisV

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

47. rickjbr

across the y axis, yes

48. ChrisV

thanks

49. rickjbr

np