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Formula Sheet

Continuity And Differentiability — Formula Sheet

IISER Aptitude Test · Mathematics

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

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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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Formula Sheet — Continuity And Differentiability

Important formulas and equations from Continuity And Differentiability for IISER Aptitude Test Mathematics.

Formulas — Continuity And Differentiability

Continuity

lim(h→0) f(a+h) = lim(h→0) f(a-h) = f(a)
lim(x→a) f(x) = f(a)

Differentiability

f'(a) = lim(h→0) [f(a+h) - f(a)]/h
LHD = lim(h→0) [f(a-h) - f(a)]/(-h)
RHD = lim(h→0) [f(a+h) - f(a)]/h

Derivative Rules and Formulas

d/dx[f(x) ± g(x)] = f'(x) ± g'(x)
d/dx[f(x)·g(x)] = f'(x)·g(x) + f(x)·g'(x)
d/dx[f(x)/g(x)] = [f'(x)·g(x) - f(x)·g'(x)]/[g(x)]²
d/dx[f(g(x))] = f'(g(x))·g'(x)

Inverse Trigonometric Functions

d/dx(sin⁻¹x) = 1/√(1-x²)
d/dx(cos⁻¹x) = -1/√(1-x²)
d/dx(tan⁻¹x) = 1/(1+x²)
d/dx(sec⁻¹x) = 1/(|x|√(x²-1))

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Frequently Asked Questions

What topics are covered in Continuity And Differentiability for IISER Aptitude Test?
Continuity And Differentiability 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: Continuity of Functions, Differentiability of Functions, Derivatives of Inverse Trigonometric Functions, Exponential and Logarithmic Functions.
How important is Continuity And Differentiability for IISER Aptitude Test?
Continuity And Differentiability is a frequently tested chapter in IISER Aptitude Test Mathematics. Questions from this chapter appear regularly in previous year papers. There are 455 practice questions available for this chapter.
How to prepare Continuity And Differentiability 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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