Floor function

[Imum Coeli]

Question: Let f(x) be the floor function. Let A = limit as x approaches -6 of (f(x) + f(-x)). Let B = f(-6) + f(6). Find A and B.

I am not really sure what I'm supposed to be doing here. I just want to write that A=B=0 but that isn't right. If anyone could please tell me what I'm supposed to be doing that would be great.

 

[stapel]

You might find it helpful, in getting started, to graph f(x) and f(-x).

 

[DrPhil]

Question: Let f(x) be the floor function. Let A = limit as x approaches -6 of (f(x) + f(-x)). Let B = f(-6) + f(6). Find A and B.

I am not really sure what I'm supposed to be doing here. I just want to write that A=B=0 but that isn't right. If anyone could please tell me what I'm supposed to be doing that would be great.

For the limit to exist, you must the same number for A approaching x from either above or below. Find [f(x)+f(-x)] for x=-6.01 and for x=-5.99. If those are equal, you have A.

 

[HallsofIvy]

Take the two one sided limits. As x approaches -6 from below, x is between -7 and -6 so f(x)= -7. -x lies between 6 and 7 so f(-x)= 6. That is, for all x between -7 and -6, f(x)+ f(-x)= -7+ 6= -1. So what is the limit as x approaches -6 from below?

As x approaches -6 from above, x is between -6 and -5 so f(x)= -6. -x lies between 5 and 6 so f(-x)= 5. That is, for all x between -6 and -5, f(x)+ f(-x)= -6+ 5= -1. So what is the limit as x approaches -6 from above? And what, then, is the limit itself?

Of course, finding B is just a matter of evaluating the functions. What is f(x)= f(-6)? What is f(-x)= f(6)?

 

[Imum Coeli]

I currently have very limited internet access but I just wanted to say thanks to you all for your help. The question is clear to me now. Thanks.