Why does Maple evaluate $\lim_{x \to \alpha/2} \frac{x^2\alpha}{2x}$ but not $\lim_{x \to \alpha/2} \frac{x^2\alpha}{2x-\alpha}$?

Question

Why does Maple evaluate the first limit but not the second:

Answer 1

Maple doesn't have a way to indicate a limit that is $+\infty$ from one side and $-\infty$ from the other. You might try

> limit(a*x^2/(2*x-a),x=a/2, right) assuming a > 0;

$$ \infty $$

> limit(a*x^2/(2*x-a),x=a/2, left) assuming a > 0;

$$-\infty $$