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Formula Sheet

Limits

ICSE · Class 11 · Mathematics

All formulas from Limits in ICSE Class 11 Mathematics. Key equations, constants, and identities for board exam preparation.

60 questions31 flashcards5 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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14 Formulas · 4 Sections

Formulas

1. Core Idea and Notation

lim_{x→c} f(x)

lim_{x→c+} f(x)

lim_{x→c-} f(x)

lim_{x→c} f(x) exists if and only if lim_{x→c+} f(x) and lim_{x→c-} f(x) both exist and are equal

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

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Frequently Asked Questions

What are the important topics in Limits for ICSE Class 11 Mathematics?
Key topics in Limits include Mind map showing diverse real-world applications of limit concepts across different fields, Limits Classification and Methods, Limits: Methods and Applications Overview. These are the concepts ICSE Class 11 examiners draw on most — study them first, then practise related questions.
How to score full marks in Limits — ICSE Class 11 Mathematics?
Understand the core concepts first, then work through the 60 practice questions available for this chapter. Revise formulas and 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.

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All 18 chapters — ICSE Class 11 Mathematics Formula Sheet

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