||x|| refers to the greatest integer function

lim (||x||-x^2)
x-3^negative

Question

||x|| refers to the greatest integer function

lim (||x||-x^2)
x->3^negative

anonymous · Answer

What's $\|x\|$ for $x<3$ ?

anonymous · Answer

what does x->3^negative mean

anonymous · Answer

$x\to3^-$, or "x approaches 3 from the left."

anonymous · Answer

@HemerickLee, directly substituting works, you just have to consider what the greatest integer function gives you for values of x less than (but close to) 3.

anonymous · Answer

-7 is the answer

anonymous · Answer

But how would you know what the answer is even with the 3-

anonymous · Answer

When u square a number assume it to b a whole no.

anonymous · Answer

$$\lim_{x\to3^-}\left(\|x\|-x^2\right)=\lim_{x\to3^-}\|x\|-\lim_{x\to3^-}x^2$$
For the first limit, you find the greatest integer for values of $x$ less than but close to 3, which would mean
$$\|2.9\|=\|2.99\|=\|2.999\|=\cdots=2$$

anonymous · Answer

Ok, then what would we have to do next

anonymous · Answer

The other limit is pretty clear. $x^2=9$ when $x\to3$.

So 2-9 is?

anonymous · Answer

-7................................. But for the first one then it would be 2 and the second on it would be -7 but then what would it be to the left

anonymous · Answer

-7 .... as simple... dats wot i wrote earlier

anonymous · Answer

I know but I needed to know how to work through it. Thank you @frnd and @SithsAndGiggles

anonymous · Answer

welcome dear HemerickLee