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Formula Sheet

Limits And Derivatives — Formula Sheet

IISER Aptitude Test · Mathematics

Free Limits And Derivatives formula sheet for IISER Aptitude Test Mathematics 2026 — all important formulas, equations, and constants for quick reference.

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An infographic summarizing the fundamental rules for derivatives of sum, difference, product (Leibnitz rule), and quotient of functions.
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Formula Sheet — Limits And Derivatives

Important formulas and equations from Limits And Derivatives for IISER Aptitude Test Mathematics.

Formulas — Limits And Derivatives

Limits - Basic Definition and Evaluation

lim_{x→a} f(x) = l
lim_{x→a⁻} f(x) = lim_{x→a⁺} f(x) = l
lim_{x→∞} (a₀xᵐ + ...)/(b₀xⁿ + ...) = a₀/b₀ if m=n

Standard Limits - Trigonometric

lim_{x→0} (sin x)/x = 1
lim_{x→0} (tan x)/x = 1
lim_{x→0} (1-cos x)/x = 0
lim_{x→0} (1-cos x)/x² = 1/2

Exponential and Logarithmic Limits

lim_{x→0} (e^x - 1)/x = 1
lim_{x→0} (a^x - 1)/x = ln a
lim_{x→0} ln(1+x)/x = 1
lim_{x→0} (1+x)^(1/x) = e

Derivatives - First Principles

f'(x) = lim_{h→0} [f(x+h) - f(x)]/h
f'(a) = lim_{x→a} [f(x) - f(a)]/(x - a)
f'(x) = lim_{h→0} [f(x+h) - f(x-h)]/(2h)

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Frequently Asked Questions

What topics are covered in Limits And Derivatives for IISER Aptitude Test?
Limits And Derivatives is an important chapter in IISER Aptitude Test Mathematics. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: 12.1 Introduction to Limits, 12.2 Algebra of Limits, 12.3 Limits of Polynomial and Rational Functions, 12.4 Trigonometric Limits.
How important is Limits And Derivatives for IISER Aptitude Test?
Limits And Derivatives is a frequently tested chapter in IISER Aptitude Test Mathematics. Questions from this chapter appear regularly in previous year papers. There are 393 practice questions available for this chapter.
How to prepare Limits And Derivatives for IISER Aptitude Test?
Start by understanding the core concepts, then solve practice questions. Focus on formulas and their applications. Use revision notes for quick review before the exam.

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