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Formula Sheet

Continuity and Differentiability — Formula Sheet

ICSE · Class 12 · Mathematics

9 formulas from Continuity and Differentiability (ICSE Class 12 Mathematics) on one page, grouped by topic. Part of the ICSE Class 12 Mathematics syllabus.

105 questions29 flashcards9 formulas & key relations5 concepts

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A graph of a continuous function at a specific point, showing the limit approaching the function value, illustrating that the function is unbroken and defined at that point.
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9 Entries · 3 Sections

Formulas and Key Relations

1. Limits and One-Sided Limits

lim_{x→c} f(x)

lim_{x→c+} f(x)

lim_{x→c-} f(x)

lim_{x→c} f(x) exists iff lim_{x→c+} f(x) = lim_{x→c-} f(x)

lim_{x→0}(sin x / x)=1

2. Continuity at a Point

lim_{x→c} f(x) = f(c)

4. Differentiability at a Point

lim_{x→c}((f(x)-f(c))/(x-c)) = f'(c)

Rf'(c) = lim_{h→0}((f(c+h)-f(c))/h)

Lf'(c) = lim_{h→0}((f(c-h)-f(c))/(-h))

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Frequently Asked Questions

What are the important topics in Continuity and Differentiability for ICSE Class 12 Mathematics?
Key topics in Continuity and Differentiability include Limits and One-Sided Limits, Continuity at a Point and on an Interval, Algebra of Continuous Functions, Differentiability at a Point and One-Sided Derivatives. Study these first, then practise questions on each for the ICSE Class 12 board exam.
How many formulas are in Continuity and Differentiability?
This sheet lists 9 formulas from Continuity and Differentiability, grouped by topic. Learn what each symbol stands for so you can apply the formula, not just recall it.
How should I revise Continuity and Differentiability for the ICSE Class 12 board exam?
Learn the core ideas first, then work through the 105 practice questions on Continuity and Differentiability. 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 Continuity and Differentiability

All ICSE Class 12 Mathematics Formula Sheet

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