lim([x]/[x])=? when x ------>0+?

Question

I mean the greatest integer function
as you may write it [[x]] but here in my country we show it by [x]

Answer 1

I know the greatest integer function as the "floor" function, and I normally see it written as └x┘, except that the └ ┘symbols would extend to the bottom of the line. I'll use [x] for the greatest integer function, for convenience.

This limit does not exist. x --> 0+ means that we approach 0 from the positive x-axis. [x] is equal to 0 for all values of 0 <= x < 1, so [x]/[x] doesn't just have a point discontinuity at x = 0; it's undefined for all values of x less than 1, and is only defined again when x < 0. Even though [x]/[x] = 1 for all values of x where [x] is defined, the limit does not exist for x --> 0+ because [x]/[x] is not defined for values arbitrarily close to x = 0 on the positive side, which would be required for the limit to exist.

Answer 2

x/x =1 for all values except for x=0. So, x=1 in one extremity, and x=0 in the other. The 'graph' is a straight line. There is no limit- it is constant 1 all the way !

Answer 3

lim (x/x) is equal to 1.
x -> 0+

Since this question is surprisingly easy, doyou mean something else when you have [x]/[x]? Maybe you mean the greatest integer function, [[ x ]]? Or maybe you instead meant x/|x| (x over the absolute value of x)?

Answer 4

xisxmultiplied by x+0=x

Answer 5

zero is the answer