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

- anonymous

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

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- anonymous

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

- anonymous

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

- anonymous

yea i have seen graphs of these functions

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- anonymous

looks sorta like steps

- anonymous

yes

- anonymous

but i have no idea how to graph one myself

- anonymous

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

- anonymous

which according to the book is 8

- anonymous

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

- anonymous

they need a grapher on this site

- anonymous

yes from the left

- anonymous

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

- anonymous

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

- anonymous

you have to take into account the -7

- anonymous

yes, so -4 overall

- anonymous

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

- anonymous

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

- anonymous

oh i know why

- anonymous

i missed a 5 lol

- anonymous

5[[x]]-7

- anonymous

so to graph this

- anonymous

yes, so 5(3)-7=8

- anonymous

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

- anonymous

yes i understnad that

- anonymous

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

- anonymous

nope i dont

- anonymous

i know what they look like

- anonymous

but not how to graph one given an equation

- anonymous

|dw:1329178784965:dw|

- anonymous

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

- anonymous

for 0-3

- anonymous

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

- anonymous

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

- anonymous

oops 1,1

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

i mean <=1

- anonymous

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

- 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]]

- anonymous

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

- anonymous

so an open circle

- anonymous

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

- 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)?

- anonymous

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

- anonymous

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

- anonymous

across the y axis, yes

- anonymous

thanks

- anonymous

np

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