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



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

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

ChrisV
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yea i have seen graphs of these functions

ChrisV
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looks sorta like steps

rickjbr
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yes

ChrisV
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but i have no idea how to graph one myself

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

ChrisV
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which according to the book is 8

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

ChrisV
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they need a grapher on this site

ChrisV
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yes from the left

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

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

ChrisV
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you have to take into account the 7

rickjbr
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yes, so 4 overall

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

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

ChrisV
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oh i know why

ChrisV
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i missed a 5 lol

ChrisV
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5[[x]]7

ChrisV
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so to graph this

rickjbr
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yes, so 5(3)7=8

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

ChrisV
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yes i understnad that

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

ChrisV
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nope i dont

ChrisV
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i know what they look like

ChrisV
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but not how to graph one given an equation

rickjbr
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dw:1329178784965:dw

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

rickjbr
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for 03

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

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

ChrisV
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oops 1,1

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

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

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

ChrisV
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i mean <=1

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

rickjbr
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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]]

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

rickjbr
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so an open circle

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

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

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

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

rickjbr
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across the y axis, yes

ChrisV
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thanks

rickjbr
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np