Mathematics · JEE

Limit, Continuity and Differentiability Concepts for JEE

91+ syllabus-aligned questions available

Quick answer

Master Limit, Continuity and Differentiability by understanding definitions, standard results, and typical JEE question patterns — then practise with syllabus-aligned MCQs on Goodmarks.

Build clear conceptual foundations for Limit, Continuity and Differentiability before speed practice. This guide covers what JEE expects and how to test yourself with MCQs.

Concept explainer

Concept overview for Limit, Continuity and Differentiability covering 9 JEE syllabus subtopics including Real-valued functions, algebra of functions, Polynomial, rational, trigonometric, logarithmic and exponential functions, Inverse functions.

Key points

Understand the definition and scope of Real-valued functions, algebra of functions in the JEE syllabus
Memorise key formulas and standard results linked to Real-valued functions, algebra of functions
Practise 20–40 syllabus-aligned MCQs with step-by-step solutions
Understand the definition and scope of Polynomial, rational, trigonometric, logarithmic and exponential functions in the JEE syllabus
Memorise key formulas and standard results linked to Polynomial, rational, trigonometric, logarithmic and exponential functions
Practise 20–40 syllabus-aligned MCQs with step-by-step solutions

JEE tips

Revise Real-valued functions, algebra of functions with a one-page formula sheet before attempting mixed tests
After each practice set, log mistakes specific to Real-valued functions, algebra of functions and reattempt after 48 hours
Revise Polynomial, rational, trigonometric, logarithmic and exponential functions with a one-page formula sheet before attempting mixed tests
After each practice set, log mistakes specific to Polynomial, rational, trigonometric, logarithmic and exponential functions and reattempt after 48 hours

Common trap

Students often rush Real-valued functions, algebra of functions questions without checking units, sign conventions, or boundary conditions — always verify assumptions before calculating.

JEE Formula Sheet

68+ important formulas for Limit, Continuity and Differentiability

View formula sheet

Subtopics in Limit, Continuity and Differentiability

View Limit, Continuity and Differentiability formula sheet — 68+ JEE formulas

Free sample questions

Attempt 8 free MCQs for Limit, Continuity and Differentiability. Unlock 83+ more with Pro.

Unlock full bank

Q1MathsUnit 7: Limit, Continuity and Differentiability

If the radius of a sphere is measured as

9 \mathrm{cm}

with an error of

0.03 \mathrm{cm}

then, find the approximate error in calculating its volume

Q2MathsUnit 7: Limit, Continuity and Differentiability

Let

\boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}-\boldsymbol{x}^{2}+\boldsymbol{x}+\mathbf{1}

and

\boldsymbol{g}(\boldsymbol{x})=

\left\{\begin{array}{l}\max \{f(t)\}, \quad 0 \leq t \leq x \quad 0 \leq x \leq 1 \\ 3-x, \quad 1<x \leq 2\end{array}\right.

Then in the interval

[0,2], g(x)

is This question has multiple correct options

Q3MathsUnit 7: Limit, Continuity and Differentiability

5.63 \times 11

is equal to

Q4MathsUnit 7: Limit, Continuity and Differentiability

If the ratio of base radius and height of a cone is 1: 2 and percentage error in radius is

\lambda \%,

then the error in its volume is

Q5MathsUnit 7: Limit, Continuity and Differentiability

Function

\boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{x}+\mathbf{2}) \boldsymbol{e}^{-\boldsymbol{x}}

Q6MathsUnit 7: Limit, Continuity and Differentiability

The two curves

x^{3}-3 x y^{2}+2=0

and

\mathbf{3} \boldsymbol{x}^{2} \boldsymbol{y}-\boldsymbol{y}^{3}-\boldsymbol{2}=\mathbf{0}

Q7MathsUnit 7: Limit, Continuity and Differentiability

Equation of normal drawn to the graph of the function defined as

f(x)=\frac{\sin x^{2}}{x}

\boldsymbol{x} \neq \mathbf{0}

and

\boldsymbol{f}(\mathbf{0})=\mathbf{0}

at the origin is?

Q8MathsUnit 7: Limit, Continuity and Differentiability

If a monomial

\frac{2}{5} x^{2} y^{2},

binomial

2 x+3 y

and a trinomial

2 x+3 y+4 z

are added, then the resultant expression is

a

Want unlimited Limit, Continuity and Differentiability practice?

Pro unlocks the full question bank, topic filters, and attempt history.

Get started free View Pro plans

Frequently asked questions

What concepts in Limit, Continuity and Differentiability are essential for JEE?

Focus on core ideas across Real-valued functions, algebra of functions, Polynomial, rational, trigonometric, logarithmic and exponential functions, Inverse functions, Graphs of simple functions, and more. JEE tests application, not just memorisation.