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Long answer·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

A school club models the cost difference between two printing plans by D(x)=x2−9x−3D(x)=\frac{x^2-9}{x-3} rupees per copy, where xx is near 3.3.
Total: 5 marks

(a) Explain why direct substitution at x=3x=3 is not enough. (1 mark)

(b) Simplify D(x)D(x) for x≠3x\ne3. (2 marks)

(c) Find the limiting cost difference as x→3x\to3. (2 marks)

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cbse-math-11.u4.t4-1.laq.004

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