Main content

AP®︎/College Calculus AB

Lesson 14: Connecting infinite limits and vertical asymptotes

Infinite limits: algebraic

AP.CALC: LIM‑2 (EU), LIM‑2.D (LO), LIM‑2.D.1 (EK), LIM‑2.D.2 (EK)

You might need: Calculator

Let f, left parenthesis, x, right parenthesis, equals, start fraction, 3, divided by, x, end fraction.

Select the correct description of the one-sided limits of f at x, equals, 0.

(Choice A)
limit, start subscript, x, \to, 0, start superscript, plus, end superscript, end subscript, f, left parenthesis, x, right parenthesis, equals, plus, infinity and limit, start subscript, x, \to, 0, start superscript, minus, end superscript, end subscript, f, left parenthesis, x, right parenthesis, equals, plus, infinity
(Choice B)
limit, start subscript, x, \to, 0, start superscript, plus, end superscript, end subscript, f, left parenthesis, x, right parenthesis, equals, plus, infinity and limit, start subscript, x, \to, 0, start superscript, minus, end superscript, end subscript, f, left parenthesis, x, right parenthesis, equals, minus, infinity
(Choice C)
limit, start subscript, x, \to, 0, start superscript, plus, end superscript, end subscript, f, left parenthesis, x, right parenthesis, equals, minus, infinity and limit, start subscript, x, \to, 0, start superscript, minus, end superscript, end subscript, f, left parenthesis, x, right parenthesis, equals, plus, infinity
(Choice D)
limit, start subscript, x, \to, 0, start superscript, plus, end superscript, end subscript, f, left parenthesis, x, right parenthesis, equals, minus, infinity and limit, start subscript, x, \to, 0, start superscript, minus, end superscript, end subscript, f, left parenthesis, x, right parenthesis, equals, minus, infinity

Stuck?