lim x?0+ (8/x - 8/|x|)

Question

lim x→0+ (8/x − 8/|x|)

Answer 1

I'll just give you a clue.

Define (piecewise) for x>0, in which case the value is always zero because the two terms are identical.

But for x<0, define the expression as 2•8/x  because you replace absolute value of x by -x and that gives you a sum (note that in this consideration x will approach zero ALWAYS THROUGH NEGATIVE values...so what's that left-side limit at 0?

 

End of rather broad hint.