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Case study·Hard exam skill (4/5)·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

In a small-angle experiment, a unit-circle sector is used to compare chord height and arc angle xx in radians.
Total: 4 marks

(a) State the standard limit connecting sin⁡x\sin x and xx as x→0x\to0. (1 mark)

(b) Find lim⁡x→0tan⁡xsin⁡x\lim_{x\to0}\frac{\tan x}{\sin x}. (1 mark)

(c) Use the result to decide whether tan⁡x\tan x and sin⁡x\sin x are nearly equal for very small xx. (2 marks)

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cbse-math-11.u4.t4-2.case.005

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