Mastering Limit Problems: [[x]] + [[-x]] with Integer n | Expert Tips and Tricks

[CrossFit415]

lim x --> n ([[x]] + [[-x]]) where n is an integer and [[ ]] is the greatest-integer function.




How would I go on about this?

Would I have to plug in n for x? So i got ([[n]] + [[-n]])

 

[Mark44]

lim x --> n ([[x]] + [[-x]]) where n is an integer and [[ ]] is the greatest-integer function.




How would I go on about this?

Would I have to plug in n for x? So i got ([[n]] + [[-n]])

I think that your first steps would be to graph y = [[x]] and y = [[-x]], and then graph y = [[x]] + [[-x]].

 

[CrossFit415]

So this would be a step function? How would I graph this if there's no numbers involved?

 

[Mark44]

Yes, the greatest integer function is a step function. Do you know what the graph looks like? Do you know what the graph of y = [[-x]] looks like. Graph both, and then the graph of y = [[x]] + [[-x]].

Why is it a problem "if there's no numbers involved"?