Question

what does the greatest integer function mean?

Answer 1

Also known as the floor function, it outputs the largest integer that is less than its input. Thus: \[\lfloor 5.8\rfloor = 5\]The graph of the function \[y=\lfloor x \rfloor\] is as follows:

Answer 2

\[\lim_{x \rightarrow 3} (2 - [| -x |]\]

Answer 3

please do that with clarification

Answer 4

The limit does not exist as there is a discontinuity at x=3. If it were a sided limit, the case would be different, however.

Answer 5

Ya, what values you plug in for the greatest integer function when x approaches to 3 from both sides +ve and -ve

Answer 6

Since \[\lfloor x \rfloor\]is constant all x such that \[a<x<a+1 \text{ where } a \in \mathbb Z\], you can plug in any value to the left or right that is less than 1 unit away from the target value, given that the target value is an integer, which it is here. If the target value is not a integer, then just plug and evaluate as there won't be any discontinuities for nonintegers. Does that make sense?

Answer 7

u mean for value to the left I plug in -4 and for value to the right I plug in -3... I dint get it.. please help me with this... The answer is right before me in the textbook
but I dont get it.