Question

Find lim and lim
x->infinity x-> -infinity
What do I do with the absolute values?

Answer 1

for the absolute values functions, you have to do one sided limits so
\(\bf lim_{x\rightarrow +\infty}\cfrac{2x-1}{|x|-3}
\implies lim_{x\rightarrow +\infty^-}\cfrac{2x-1}{-x-3}\)


so, if we're going towards the positive infinity, you can't approach it from the right, so only from the left

Answer 2

if it was a fixed value, other than infinity, then we'd do a one-sided limit check for each scenario

Answer 3

Thanks.