Business Mathematics, Logical Reasoning and Statistics
Differential and Integral Calculus
5% weightage

Indeterminate Forms

Complete study guide with 5 practice questions, detailed explanations, and expert solutions for Indeterminate Forms in CA Foundation Business Mathematics, Logical Reasoning and Statistics.

Practice Questions

5
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Hard
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Study Notes: Indeterminate Forms

Free study material for CA Foundation Business Mathematics, Logical Reasoning and StatisticsDifferential and Integral Calculus

Indeterminate forms (0/0, ∞/∞, 0×∞, ∞-∞, 0⁰, 1^∞, ∞⁰) require algebraic manipulation. Techniques: (1) Factorization: lim(x→2) [(x²-4)/(x-2)] = lim [(x-2)(x+2)/(x-2)] = 4; (2) Rationalization: Multiply by conjugate; (3) Substitution: Let u = new variable; (4) L'Hôpital's rule: If lim f/g is 0/0 or ∞/∞, then lim f/g = lim f'/g'. Example 0/0: lim(x→0) [sin x / x]. Use standard limit = 1. Example ∞/∞: lim(x→∞) [3x²/(2x²+1)] = 3/2 (divide by highest power). Exam tip: Identify indeterminate form first. Choose appropriate technique. Verify result is reasonable.

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