AP®MathsCollege BoardCalculus ABExam QuestionsUnit 1: Limits & ContinuityLimits

Limits (College Board AP® Calculus AB)

Exam Questions

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Limits

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Limits

1
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Graph of function 'f' with a filled point at (1,-2) and open points at (1,1) and (2,-3), illustrating the curve's changing behavior on a coordinate plane.

The graph of the function f is shown in the figure above. The value of limit as x rightwards arrow 1 to the power of plus of f open parentheses x close parentheses is

  • negative 3

  • negative 2

  • 1

  • nonexistent

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2
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A graph labeled "Graph of f" plotting points (1,3), (2,1), (3,3), (4,5), (5,3), and (6,5) on a grid, with x-axis from 0 to 6, y-axis from 0 to 6.

The graph of the function f is shown above. Which of the following statements is false?

  • limit as x rightwards arrow 2 of f open parentheses x close parentheses exists.

  • limit as x rightwards arrow 3 of f open parentheses x close parentheses exists.

  • limit as x rightwards arrow 5 of f open parentheses x close parentheses exists.

  • The function is continuous at x equals 4.

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3
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The line y equals 3 is a horizontal asymptote to the graph of which of the following functions?

  • y equals fraction numerator 1 over denominator x minus 3 end fraction

  • y equals 3 x

  • y equals fraction numerator x minus 15 x squared over denominator 13 minus 5 x squared end fraction

  • y equals fraction numerator 3 x over denominator 7 minus x end fraction

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4
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If f open parentheses x close parentheses equals open curly brackets table row cell ln x space space space space space space for space 0 less than x less or equal than 3 end cell row cell x ln 3 space space space space for space 3 less than x less or equal than 5 end cell end table close, then limit as x rightwards arrow 3 of f open parentheses x close parentheses is

  • ln 3

  • ln 27

  • 1 third

  • nonexistent

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5
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If limit as x rightwards arrow 2 of f open parentheses x close parentheses equals 5, which of the following must be true?

I. space space f is continuous at x equals 2.

II. space space f is differentiable at x equals 2.

III. space space f open parentheses 2 close parentheses equals 5

  • None

  • I only

  • I and III only

  • I, II and III

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