What is the notation for the right-hand limit as x approaches a?

What is the notation for the right-hand limit as x approaches a?

• A. lim_{x->a^+} f(x) = L.
• B. lim_{x->a^-} f(x) = L.
• C. lim_{x->a} f(x) = L.
• D. lim_{x->a^*} f(x) = L.

Answer: (A)

Right-hand limit means we're approaching a from values greater than a, so x is just a bit larger than a as it gets closer. The notation lim_{x->a^+} f(x) = L encodes that direction: the plus sign shows we’re coming from the right side. If we were approaching from the left, we’d use lim_{x->a^-} f(x) = L. A two-sided limit lim_{x->a} f(x) = L describes the value both sides would converge to, but it only exists if the right- and left-hand limits agree. The form lim_{x->a^*} f(x) isn’t standard notation. So this right-hand notation is the correct way to express the limit from the right.

Right-hand limit means we're approaching a from values greater than a, so x is just a bit larger than a as it gets closer. The notation lim_{x->a^+} f(x) = L encodes that direction: the plus sign shows we’re coming from the right side. If we were approaching from the left, we’d use lim_{x->a^-} f(x) = L. A two-sided limit lim_{x->a} f(x) = L describes the value both sides would converge to, but it only exists if the right- and left-hand limits agree. The form lim_{x->a^*} f(x) isn’t standard notation. So this right-hand notation is the correct way to express the limit from the right.