FRQ — Limits and Continuity

Free response·Standard multi-step (3/5)·No calculatorNeeds mentor review

Difficulty guide

The label describes the problem, not your ability.

1/5 - Foundational

Warm-up setup; checks one basic idea.

2/5 - Routine exam skill

Normal syllabus skill; usually one main rule or interpretation.

3/5 - Standard multi-step

Exam-style problem with multiple steps or a common trap.

4/5 - Hard exam skill

High-end exam problem; combines methods carefully.

5/5 - Challenge

Stretch problem beyond normal exam pressure.

Question

\lim_{

x\to a}f(x)=2

,\quad \lim_{

x\to a}g(x)=-3

,\quad \lim_{

x\to a}h(x)=0

Total: 6 points

(a) Find $\lim_{x\to a}(4f(x)+g(x)^2)$ . (2 points)

(b) Find $\lim_{x\to a}\frac{f(x)-g(x)}{f(x)+1}$ and justify that the quotient law applies. (2 points)

(c) Explain why the given information is not enough to evaluate $\lim_{x\to a}\frac{f(x)}{h(x)}$ using the quotient law. (2 points)

Your response (optional — you can also work on paper)

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