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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

F(x)=x2sin⁡(3x),x≠0F(x)=x^2\sin\left(\frac{3}{x}\right),\quad x\ne0
Total: 5 points

(a) Write an inequality that bounds sin⁡(3/x)\sin(3/x). (1 point)

(b) Use your inequality to bound F(x)F(x) between two simpler functions. (2 points)

(c) Use the squeeze theorem to evaluate lim⁡x→0F(x)\lim_{x\to0}F(x). (2 points)

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