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AP Calculus BC 1.5 Continuity and Limits Question Bank

Use limit theorems and algebraic properties to evaluate one-sided and two-sided limits and decide when a limit does not exist.

Syllabus
Effective Fall 2025
Course
AP Calculus BC

Exam points

  • interpret limits and end behavior from algebraic or graphical evidence
  • use one-sided limits and continuity conditions to justify conclusions

Covered syllabus points

LIM-1.D—Determine the limits of functions using limit theorems

1.5 Determining Limits Using Algebraic Properties of Limits question 1

[Maximum number: 1]

The functions f(x), g(x), and h(x) have derivatives of all orders. Listed above are values for the functions and their first and second derivatives at x=3. Find lim⁡x→3(f(x))2−3h(x)g(x)+h(x)\lim _{x \rightarrow 3} \frac{(f(x))^{2}-3 h(x)}{g(x)+h(x)}.

A

−15-\frac{1}{5}

B

12\frac{1}{2}

C

1

D

nonexistent

Figure for Question 1.5 Determining Limits Using Algebraic Properties of Limits question 1 — AP Calculus BC
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