Question

What is the behavior of the function as x approaches zero form the right?

y approaches - infinity
y approaches zero

y approaches + infinity

Answer 1

I can’t tell which of those three is correct without the function (or its graph). Please paste the expression or an image of the graph.

Meanwhile, here are quick rules you can use to decide the right-hand behavior yourself:

- If f is defined at 0 and continuous there, lim{x→0+} f(x) = f(0) (a finite number).
- If the denominator → 0 while the numerator → nonzero, the limit is infinite; the sign (±∞) comes from the signs of numerator and denominator as x→0+.
- If numerator and denominator both → 0, simplify (factor, cancel), or use L’Hôpital’s rule / series to find a finite limit or ±∞.
- If f(x) = x^a: for a>0, limit = 0; for a<0, magnitude → ∞ and the sign follows the coefficient.
- If f(x) = ln x, lim{x→0+} ln x = −∞.
- For 1/x as x→0+: +∞; for −1/x as x→0+: −∞; for x or x^2 as x→0+: 0.

Send the function (or graph) and I’ll compute the right-hand limit and state whether y→−∞, 0, or +∞.