Question

||x|| refers to the greatest integer function

lim x-> 3 (from the left) of..
(||x||-x^2)= ?

Answer 1

when x->3 from left (also called \(3^-\))
x is very very near to 3, but LESS than 3
so, what you think will be the value of ||x||, when x= \(3^-\)

Answer 2

and you know what is greatest integer function, right ?

Answer 3

nope :x That's the reason I posted this question up here. not sure what that means xD

Answer 4

ohhh..
greatest integer function is also called floor function,
it is the largest integer not greater than x.

so, ||+5.4|| will 5 because its not greater than 5.4 and its largest among, 5,4,3,2,....

Answer 5

got that ?

Answer 6

Mmmm gotcha
so I'd subsitute 2 instead?

Answer 7

you got it :)
||\(3^-\)|| = 2

Answer 8

so the value of limit will be ?

Answer 9

-7 :b

Answer 10

correct :)

Answer 11

Thanks a bunch. Quick question, for another question...
lim x->0 from the left of
(x-2sqrt(x)+1)/(sqrt(x)-1) = ?
I simplified to get sqrt(x) -1 = ?
but what happens since when substituting x it's taking the radical of a negative number? should I just count it as zero? Does the limit not exist?

Answer 12

after you are left with sqrt x-1
you can directly plug in x=0

Answer 13

don't I need to plug in the -.0001 though? I mean just plugging in zero makes sense but thought it'd go against the steps you're meant to take

Answer 14

while taking the limit, we always plug in that number,
like if x->+4 from right, we won't plug in 4.00001, we will plug in 4 only.
+4 from right means values near to and greater than 4, yes, but while evaluating the limit, we just plug in 4.

Answer 15

and interpretation of your question will be
as x tends to 0 from left
(x-2sqrt(x)+1)/(sqrt(x)- 1) tends to -1

Answer 16

gotcha