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lim x>4- ([[x]]-7)

Mathematics
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\[\lim_{x \rightarrow 4-} ([[x]] -7)\]
greatest integer function, it will be a horizontal line from (3<=x<4)
yea i have seen graphs of these functions

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Other answers:

looks sorta like steps
yes
but i have no idea how to graph one myself
i am assuming if I graphed this I could see the limit
which according to the book is 8
You're approaching x=4 from the left, correct?
they need a grapher on this site
yes from the left
If you're approaching 4 from the left, [[x]] will be 3
so how to i determine the points i need to plot on [[x]]-7
you have to take into account the -7
yes, so -4 overall
It's just the graph of f(x)=[[x]] shifted down 7 units
well the book says 8 so .... >.<
oh i know why
i missed a 5 lol
5[[x]]-7
so to graph this
yes, so 5(3)-7=8
If you were approaching from the right, [[x]] would be 4
yes i understnad that
so you don't know how to graph the greatest integer function?
nope i dont
i know what they look like
but not how to graph one given an equation
|dw:1329178784965:dw|
that is f(x)=[[x]]
for 0-3
yea how do i know to start at 0 and stop 1
then start at 1,2 and stop at 2,1
oops 1,1
greatest integer function definition, [[x]] is the greatest integer less than or equal to x
f(x)=[[x]] f(3.999999999999999999999)=3 f(3)=3 f(4)=4
so by definition if x=1 then [[x]] is x>= 1
i mean <=1
if x=1, [[x]]=1
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]]
but you're not actually starting at [[x]] + 1
so an open circle
it is defined at all integers, but not continuous at any integer
so if I were doing 5[[4]]-7 i would plot from (4,13) t0 (5,13) with an open point at (5,13)?
yes, open circle at (5,13), closed at (4,13)
and if it happened to be [[-x]] i would just reflect
across the y axis, yes
thanks
np

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