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AP Calculus AB 1.8 Determining Limits Using the Squeeze Theorem Question Bank

Practise AP Calculus AB 1.8 squeeze-theorem questions by connecting bounding functions, limit values and continuity.

Syllabus
Effective Fall 2025
Course
AP Calculus AB

Exam points

  • identify matching upper and lower limits that force an unknown function limit
  • justify continuity by combining the squeeze theorem with the function value

Covered syllabus points

LIM-1.E—Determine the limits of functions using equivalent expressions for the function or the squeeze theorem—Topic 1.8

1.8 Determining Limits Using the Squeeze Theorem question 1

[Maximum number: 1]

Let f and g be the functions defined by f(x)=x2−25x2−29f(x)=\frac{x^{2}-25}{x^{2}-29} and g(x)=x+52x+4g(x)=\frac{x+5}{2 x+4}. If the function h satisfies f(x)≤h(x)≤g(x)f(x) \leq h(x) \leq g(x) for 1≤x≤51 \leq x \leq 5, what is lim⁡x→3h(x)\lim _{x \rightarrow 3} h(x) ?

A

12\frac{1}{2}

B

45\frac{4}{5}

C

1

D

The limit cannot be determined from the given information.

Figure for Question 1.8 Determining Limits Using the Squeeze Theorem question 1 — AP Calculus AB
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