Maths Volume-7 Part II(Continuity and Differentiability)

Synopsis of Continuity and Differentiability - I

Description: Functions' smoothness, limits, derivatives, and their interrelation define continuity and differentiability concepts.

Synopsis of Continuity and Differentiability - II

Description: Differentiability implies continuity, but continuity doesn’t guarantee differentiability; includes derivative applications.

Graphical Transformation

Description: Scaling, shifting, reflecting, and rotating graphs help visualize function behavior and transformations.

Definition of Continuity - I

Description: A function is continuous if its limit, function value, and approach value match.

Definition of Continuity - II

Description: Continuous functions have no abrupt jumps or breaks in their domain.

Definition of Continuity - III

Description: Mathematically, continuity requires at every point.

Definition of Continuity - IV

Description: Discontinuous functions show gaps, asymptotes, or sudden jumps in values.

Continuity at a Point - I

Description: A function is continuous at if limits exist and match .

Continuity at a Point - II

Description: Pointwise continuity ensures no abrupt changes in function values at specific points.

Continuity at a Point - III

Description: Checking one-sided limits confirms continuity by matching left-hand and right-hand limits.

Continuity for Composition of Function - I

Description: For composition continuity, if and are continuous, then is continuous.

Continuity for Composition of Function - II

Description: A continuous inner function and a continuous outer function ensure overall continuity in composition.

Continuity for Composition of Function - III

Description: A function is differentiable at a point if its derivative exists at that point.

Differentiability at a point - I

Description: Differentiability requires the function to be continuous and have equal left-hand and right-hand derivatives.

Differentiability at a point - II

Description: If a function has a sharp corner or cusp, it is not differentiable there.

Differentiability at a point - III

Description: A function is differentiable in an interval if it is differentiable at every point inside.

Differentiability in the interval - I

Description: Differentiability in an open interval means the function has a derivative at all interior points.

Differentiability in the interval - II

Description: If a function is differentiable in an interval, it is necessarily continuous in that interval.

Synopsis of Definite Integral - II

Description: Fundamental theorem links differentiation and integration, ensuring accurate computations in applied mathematics problems.

Basic Definition - IV

Description: Bounded functions ensure convergence, making definite integrals reliable for precise mathematical and scientific analysis.

Basic Definition - V

Description: Integral calculations require understanding limits, functions, and fundamental properties for accurate mathematical problem-solving.

Properties of Definite Integral - I

Description: Linearity allows splitting integrals, simplifying calculations and enabling easier evaluation of complex functions.

Maths Volume-5(Binomial theorem and its simple applications)

Board: CBSE

Stream: Science

Standard: XI

Course: JEE/NEET

Maths Volume-4 (Permutation and Combination)

Board: CBSE

Stream: Science

Standard: XII

Course: JEE/NEET

Physics Volume-10(Waves)

Board: CBSE

Stream: Science

Standard: XI

Course: JEE/NEET

Maths Volume-12 (Vector Algebra)

Board: CBSE

Stream: Science

Standard: XII

Course: JEE/NEET

Maths Volume-8 Part I(Indefinite Integral)

Board: CBSE

Stream: Science

Standard: XII

Course: JEE/NEET

Maths Volume-8 Part II(Definite Integral)

Board: CBSE

Stream: Science

Standard: XII

Course: JEE/NEET

Maths Volume-11(3D Geometry)

Board: CBSE

Stream: Science

Standard: XII

Course: JEE/NEET

Physics Volume-6(Mechanics-VI)

Board: State Board

Stream: Science

Standard: XII

Course: JEE/NEET

Physics Volume-8(Thermodynamics-II)

Board: CBSE

Stream: Science

Standard: XI

Course: JEE/NEET

Physics Volume-5(Mechanics-V)

Board: CBSE

Stream: Science

Standard: XI

Course: JEE/NEET

Physics Volume-9(Thermodynamics-III)

Board: CBSE

Stream: Science

Standard: XI

Course: JEE/NEET