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Formula Sheet

Indeterminate Forms — Formula Sheet

ICSE · Class 12 · Mathematics

7 formulas from Indeterminate Forms (ICSE Class 12 Mathematics) on one page, grouped by topic. Part of the ICSE Class 12 Mathematics syllabus.

127 questions27 flashcards7 formulas & key relations5 concepts

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7 Entries · 4 Sections

Formulas and Key Relations

2. 0/0 form

If lim(x→a) f(x)=0 and lim(x→a) g(x)=0, then lim(x→a) [f(x)/g(x)] is of type 0/0.

L'Hôpital's Rule for 0/0 form: If lim(x→a) f(x)=0 and lim(x→a) g(x)=0, and lim(x→a) [f'(x)/g'(x)]=l, then lim(x→a) [f(x)/g(x)] = lim(x→a) [f'(x)/g'(x)

3. ∞/∞ form

If lim(x→a) f(x)=∞ and lim(x→a) g(x)=∞, then lim(x→a) [f(x)/g(x)] is of type ∞/∞.

4. 0·∞ and ∞−∞ forms

0·∞ working rule: Step I identify 0·∞ form; Step II convert to 0/0 form or ∞/∞ form; Step III apply L'Hôpital's Rule [f(x)→0, g(x)→∞]

A limit lim(x→a) [f(x)·g(x)] is said to be of the type 0·∞ if lim(x→a) f(x)=0 and lim(x→a) g(x)=∞.

∞−∞ working rule: Step I identify ∞−∞ form; Step II combine terms to get 0/0 form or ∞/∞ form; Step III apply L'Hôpital's Rule [f(x)→∞, g(x)→∞]

Powers: 0 to the power 0, infinity to the power 0, and 1 to the power infinity

Set y = f(x)^{g(x)}, then take log y = g(x) log f(x).

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Frequently Asked Questions

What are the important topics in Indeterminate Forms for ICSE Class 12 Mathematics?
Key topics in Indeterminate Forms include Meaning of Indeterminate Forms and Basic Idea, Converting 0 times infinity and infinity minus infinity, Powers: 0 to the power 0, infinity to the power 0, and 1 to the power infinity, Important Examples and Result Patterns. Study these first, then practise questions on each for the ICSE Class 12 board exam.
How many formulas are in Indeterminate Forms?
This sheet lists 7 formulas from Indeterminate Forms, grouped by topic. Learn what each symbol stands for so you can apply the formula, not just recall it.
How should I revise Indeterminate Forms for the ICSE Class 12 board exam?
Learn the core ideas first, then work through the 127 practice questions on Indeterminate Forms. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Indeterminate Forms

All ICSE Class 12 Mathematics Formula Sheet

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