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Formula Sheet

Limits — Formula Sheet

ICSE · Class 11 · Mathematics

15 formulas from Limits (ICSE Class 11 Mathematics) on one page, grouped by topic. Part of the ICSE Class 11 Mathematics syllabus.

60 questions31 flashcards15 formulas & key relations5 concepts

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A graph of a function f(x) with a removable discontinuity (a hole) at x=a. Show arrows on the x-axis indicating x approaching 'a' from both the left and the right. Corresponding arrows on the y-axis s
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15 Entries · 5 Sections

Formulas and Key Relations

1. Core Idea and Notation

lim_{x→c} f(x)

lim_{x→c+} f(x)

lim_{x→c-} f(x)

2. Algebra of Limits

lim_{x→c}[f(x)+g(x)] = lim_{x→c}f(x) + lim_{x→c}g(x)

lim_{x→c}[f(x)-g(x)] = lim_{x→c}f(x) - lim_{x→c}g(x)

lim_{x→c}[f(x)g(x)] = lim_{x→c}f(x) · lim_{x→c}g(x)

lim_{x→c}[f(x)/g(x)] = (lim_{x→c}f(x))/(lim_{x→c}g(x)), provided lim_{x→c}g(x) ≠ 0

3. Standard Algebraic Limits and Methods

lim_{x→a}[(x^n-a^n)/(x-a)] = n a^(n-1)

lim_{x→∞}(1/x)=0; lim_{x→-∞}(1/x)=0

4. Special Trigonometric Limits

cos x < (sin x)/x < 1, for 0<|x|<π/2

lim_{x→0}(sin x/x)=1

lim_{x→0}((1-cos x)/x)=0

lim_{x→0}(tan x/x)=1

Standard Trigonometric Limits and Their Use

The key trigonometric limit is lim_{x->0}(sin x/x) = 1.

Another standard limit is lim_{x->0}((1-cos x)/x) = 0.

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Frequently Asked Questions

What are the important topics in Limits for ICSE Class 11 Mathematics?
Key topics in Limits include Core Idea of Limit, Algebra of Limits, Methods for Evaluating Algebraic Limits, Standard Trigonometric Limits and Their Use. Study these first, then practise questions on each for Class 11 exams.
How many formulas are in Limits?
This sheet lists 15 formulas from Limits, grouped by topic. Learn what each symbol stands for so you can apply the formula, not just recall it.
How should I revise Limits for Class 11 exams?
Learn the core ideas first, then work through the 60 practice questions on Limits. 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 Limits

All ICSE Class 11 Mathematics Formula Sheet

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