Limits and Graphs of Rational Functions

Introduction of Rational Functions:   Have you ever wondered why some graphs seem to have holes in them?   Why do some lines seem to approach a certain value but never quite reach it?   Rational functions are the key to understanding these phenomena and so much more.   Imagine a rollercoaster ride where the […]

Quadratic equations and its Application

Introduction Have you ever wondered how bridges can withstand the forces of nature and remain standing for years, even decades? How do economists determine the optimal level of production or sales that will maximize profits? The answer lies in quadratic equations, a fundamental mathematical concept with many applications in science, engineering, and economics. In this […]

Conservation Of Mechanical Energy

Introduction: Have you ever wondered how a toy car with a wound-up spring can move forward without any external energy source? How a bow and arrow can launch an arrow forward with incredible speed and accuracy?   These everyday objects and devices are powered by mechanical energy, which is a fundamental concept in physics that […]

Inverse Trigonometric Functions

Introduction: Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It has numerous real-world applications in physics, engineering, and architecture. Trigonometric functions such as sine, cosine, and tangent describe these relationships. Inverse trigonometric functions, also known as arc functions, are the inverse operations of trigonometric functions. […]

Collisions and Momentum

Introduction:- Have you ever wondered: How do air particles transmit sound wave energy to your ears? How do boxing gloves prevent your fist from getting injured during boxing? Why does a player pull his hands back slightly while catching the ball? And many more incidents like these. After reading this blog, you will not only […]

Integration by Parts

Integration by Parts   Integration by parts is a unique fashion of integrating two functions when they’re multiplied together or for evaluating integrals whose integrand is the product of two functions to make complicated integrations easy to break. This system is also nominated as partial integration.     Formula : Integration by Parts   The […]

Behavior of a charge in Magnetic field

Charge feels force on it. The force is dependent on the charge (q), velocity(v)and magnetic field (B). $$ F=q(v \times B) $$ $$ \mathrm{F}=\mathrm{qvB} \sin \theta $$ Let us consider this particle has a charge q and it moves in the direction of magnetic field B (motion in a magnetic field); the velocity is v […]

Exact and homogenous differential equation

We will talk about a type of ODE called the exact differential equation If the differential equation of the type $$\frac{d y}{d x}=f(x, y)$$ can be written in the form of $$M(x, y) d x+N(x, y) d y=0$$ and $$\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x} $$ then this form is called exact. The following examples clarify […]