Calculus Formula

Collection of All Calculus Formulae and Definition

Calculus Formula App contains all calculus formula along with their definition. This app is designed for students of class 11, 12 and higher. The Formulae are divided into nine categories. These are as

1. Real Number

Laws of Real Numbers

Closure, Commutative, Associative, Existence of Identity, Existence of Negatives, and Existence of Reciprocals Property

Distributive Laws

Order relation

Definition of Trichotomy, Monotonicity, Recurring Decimals, Absolute Value, Finite Intervals, Open as well as closed Intervals, and Infinite Intervals

Important Facts and Formula of Modulus

2. Limit

Definition of Neighborhood, Symmetric, Deleted, One sided Neighborhood, and Limit of a Function, Left Limit, and Right Limit

Limit of a Function

Algebra of Limits

Standard Result and Important Formulae of Limit

Limit of Rational Functions

Uniqueness Theorem

Existence of a Limit

Squeeze Principle

Method of Evaluation of Limit

L’s Hospital Rule

Important Expansions

3. Continuity

Definition of Left Continuity, Right Continuity, Continuity at a Point, and Continuity on a Set, Continuity of a Function in an Interval, Continuous Function, Domain of Continuity, and Discontinuous Function

Kinds of Discontinuity

Removable Discontinuity

Discontinuity of First and Second Kind

Algebra of Continuous Functions

4. Differentiation

Definition of Differentiation

First Principle

Derivative of Standard Functions

Product Formula of Differentiation

Division Formula of Differentiation

Chain Rule

Derivative of Trigonometric, Inverse Trigonometric, Logarithmic, and Exponential Functions

Method of Differentiation of Implicit Functions, Parametric Functions, a Function with respect to another Function, and Logarithmic Differentiation

Formula of Successive Differentiation

5. Integration

Definition of Indefinite Integral

Theorems of Indefinite Integral

Indefinite Integral of Trigonometric, Algebraic, Logarithmic, Exponential, Surds and Some Standard Functions

Method of Evaluation of special Trigonometric, Quadratic, Surd Functions, and By Partial Fraction

Integration by Parts

6. Definite Integral

Definition of Definite Integral

Fundamental Theorems of Integral Calculus

Properties of Definite Integrals

7. Application

Application of Derivative

Motion in Straight line

Vertical Motion

Condition for Monotonicity

Mean Value Theorem

Lagrange’s Theorem

Formation of Tangent and Normal Formula

Formula to calculate Length of Tangent and Normal

Condition of Maxima and Minima

Application of Definite Integrals to calculate Area under Curves

8. Differential Equation

Definition and Examples of Differential Equations, Order and Degree of Differential Equations

Method of Formation of Differential Equations

Solution of Differential Equations

Method of Solving Variable Separable, Homogeneous, Reducible to homogeneous, Linear, and Reducible to Linear Differential Equation

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